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content/posts/2018-10-26-twenty-years-of-rsa-attacks.md
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@ -2,21 +2,30 @@
title = "twenty years of attacks on rsa with examples"
date = 2018-10-26
toc = true
tags = ["crypto"]
tags = ["ctf", "crypto"]
languages = ["python"]
math = true
+++
There's [a great paper][1] I found by Dan Boneh from 1998 highlighting the weaknesses of the RSA cryptosystem. I found this paper to be a particularly enlightening read (and interestingly enough, it's been 20 years since that paper!), so here I'm going to reiterate some of the attacks described in the paper, but using examples with numbers in them. <!--more-->
There's [a great paper][1] I found by Dan Boneh from 1998 highlighting the
weaknesses of the RSA cryptosystem. I found this paper to be a particularly
enlightening read (and interestingly enough, it's been 20 years since that
paper!), so here I'm going to reiterate some of the attacks described in the
paper, but using examples with numbers in them. <!--more-->
(Also please excuse the lack of proper formatting, I've yet to figure out how to get Gutenberg to accept Latex)
That being said, I _am_ going to skip over the primer of how the RSA cryptosystem works, since there's already a great number of resources on how to do that.
That being said, I _am_ going to skip over the primer of how the RSA
cryptosystem works, since there's already a great number of resources on that.
## factoring large integers
Obviously this is a pretty bruteforce-ish way to crack the cryptosystem, and probably won't work in time for you to see the result, but can still be considered an attack vector. This trick works by just factoring the modulus, N. With N, finding the private exponent d from the public exponent e is a piece of cake.
Obviously this is a pretty bruteforce-ish way to crack the cryptosystem, and
probably won't work in time for you to see the result, but can still be
considered an attack vector. This trick works by just factoring the modulus,
$N$. With $N$, finding the private exponent $d$ from the public exponent $e$ is
a piece of cake.
Let's choose some small numbers to demonstrate this one (you can follow along in a Python REPL if you want):
Let's choose some small numbers to demonstrate this one (you can follow along in
a Python REPL if you want):
```py
>>> N = 881653369
@ -24,7 +33,9 @@ Let's choose some small numbers to demonstrate this one (you can follow along in
>>> c = 875978376
```
N is clearly factorable in this case, and we can use resources like [msieve][7] or [factordb][2] to find smaller primes in this case. Since we know now that `N = 20717 * 42557`, we can find the totient of N:
$N$ is clearly factorable in this case, and we can use resources like
[msieve][7] or [factordb][2] to find smaller primes in this case. Since we know
now that $N = 20717 \times 42557$, we can find the totient of $N$:
```py
>>> p = 20717
@ -33,7 +44,8 @@ N is clearly factorable in this case, and we can use resources like [msieve][7]
881590096
```
Now all that's left is to discover the private exponent and solve for the original message! (you can find the modular inverse function I used [here][3])
Now all that's left is to discover the private exponent and solve for the
original message! (you can find the modular inverse function I used [here][3])
```py
>>> d = modinv(e, tot)
@ -46,15 +58,28 @@ And that's it! Now let's look at some more sophisticated attacks...
## elementary attacks
These attacks are related to the _misuse_ of the RSA system. (if you can't tell, I'm mirroring the document structure of the original paper)
These attacks are related to the _misuse_ of the RSA system. (if you can't tell,
I'm mirroring the document structure of the original paper)
### common modulus
My cryptography professor gave this example as well. Suppose there was a setup in which the modulus was reused, maybe for convenience (although I suppose with libraries today, it'd actually be more _inconvenient_ to reuse the key). Key pairs would be issued to different users and they would share public keys with each other and keep private keys to themselves.
My cryptography professor gave this example as well. Suppose there was a setup
in which the modulus was reused, maybe for convenience (although I suppose with
libraries today, it'd actually be more _inconvenient_ to reuse the key). Key
pairs would be issued to different users and they would share public keys with
each other and keep private keys to themselves.
The problem here is if you have a key pair, and you got someone else's public key, you could easily derive the private key by just factoring the modulus. Let's see how this works with a real example now.
The problem here is if you have a key pair, and you got someone else's public
key, you could easily derive the private key by just factoring the modulus.
Let's see how this works with a real example now.
Since this is a big problem if you were to really use this cryptosystem, I'll be using actual keys from an actual crypto library instead of the small numbers like in the first example to show that this works on 2048-bit RSA. The library is called [PyCrypto][4], and if you're planning on doing anything related to crypto with Python, it's a good tool to have with you. For now, I'm going to generate a 2048-bit key (by the way, in practice you probably shouldn't be using 2048-bit keys anymore, I'm just trying to spare my computer here).
Since this is a big problem if you were to really use this cryptosystem, I'll be
using actual keys from an actual crypto library instead of the small numbers
like in the first example to show that this works on 2048-bit RSA. The library
is called [PyCrypto][4], and if you're planning on doing anything related to
crypto with Python, it's a good tool to have with you. For now, I'm going to
generate a 2048-bit key (by the way, in practice you probably shouldn't be using
2048-bit keys anymore, I'm just trying to spare my computer here).
```py
>>> from Crypto.PublicKey import RSA
@ -62,7 +87,10 @@ Since this is a big problem if you were to really use this cryptosystem, I'll be
<_RSAobj @0x7f3d3226dfd0 n(2048),e,d,p,q,u,private>
```
Now, normally when you generate a new key, it'd generate a new modulus. For the sake of this common modulus attack, we'll force the new key to use the same modulus. This also means we'll have to choose an exponent e other than the default choice of 65537 (see [this link][5] for documentation):
Now, normally when you generate a new key, it'd generate a new modulus. For the
sake of this common modulus attack, we'll force the new key to use the same
modulus. This also means we'll have to choose an exponent $e$ other than the
default choice of 65537 (see [this link][5] for documentation):
```py
>>> N = k1.p * k1.q
@ -78,11 +106,33 @@ Now, normally when you generate a new key, it'd generate a new modulus. For the
<_RSAobj @0x7f3d31c7c5f8 n(2048),e,d,p,q,u,private>
```
Ok, now we have two keys, `k1` and `k2`. Now I'll show how using only the public and private key of `k1` (assuming this is the pair that we got legitimately from the crypto operator), and the public key of `k2`, which is tied to the same modulus, we can find the private key of `k2`.
Ok, now we have two keys, $k_1$ and $k_2$. Now I'll show how using only the public
and private key of $k_1$ (assuming this is the pair that we got legitimately from
the crypto operator), and the public key of $k_2$, which is tied to the same
modulus, we can find the private key of $k_2$.
To do this, we'll try to find the roots of the equation `f(x) = x^2 - (p + q)x + pq`. You'll find that for values of `p` and `q`, this will produce `f(p) = p^2 - p^2 - qp + pq`, and `f(q) = q^2 - pq - q^2 + pq`. We know that `N = pq`. How can we find `p + q`? Since `phi(N) = (p - 1)(q - 1) = pq - p - q + 1`, we can find that `phi(N) = N - (p + q) + 1`, so `p + q = N - phi(N) + 1`. Now we need to use `e` and `d` to estimate `phi(N)`. Recall that `ed = 1 mod phi(N)`. This is equivalent to saying `ed = 1 + k*phi(N)`. Then `(ed - 1) / phi(N) = k`.
To do this, we'll try to find the roots of the equation:
It turns out that `k` is extremely close to `ed/N`: `ed/N = (1 + k*phi(N)) / N = 1/N + k*phi(N)/N`. `1/N` is basically 0, and `phi(N)` is very close to `N`, so it shouldn't change the value of `k` by very much. We now use `ed/N` to estimate `k`: `phi(N) = (ed - 1) / (ed / N)`.
$$ f(x) = x^2 - (p + q)x + pq $$
You'll find that for values of $p$ and $q$, this will produce $f(p) = p^2 - p^2
\- qp + pq$, and $f(q) = q^2 - pq - q^2 + pq$. We know that $N = pq$. How can we
find $p + q$? Since $\phi(N) = (p - 1)(q - 1) = pq - p - q + 1$, we can find
that $\phi(N) = N - (p + q) + 1$, so $p + q = N - \phi(N) + 1$.
Now we need to use $e$ and $d$ to estimate $\phi(N)$. Recall that $ed = 1 \mod
\phi(N)$. This is equivalent to saying $ed = 1 + k\phi(N)$. Then $\frac{ed -
1}{\phi(N)} = k$.
It turns out that $k$ is extremely close to $\frac{ed}{N}$:
$$ \frac{ed}{N} = \frac{1 + k\phi(N)}{N} = \frac{1}{N} + \frac{k\phi(N)}{N} $$
$\frac{1}{N}$ is basically 0, and $\phi(N)$ is very close to $N$, so it
shouldn't change the value of $k$ by very much. We now use $\frac{ed}{N}$ to
estimate $k$:
$$ \phi(N) = \frac{ed - 1}{\frac{ed}{N}} $$
```py
>>> from decimal import Decimal, getcontext
@ -93,7 +143,7 @@ It turns out that `k` is extremely close to `ed/N`: `ed/N = (1 + k*phi(N)) / N =
Decimal('29977270253913673973269594877868500604696844309480395834898813292056864035968758602074842333119394545818563664205865827843973433118231606201251719390934610989873635763197929136439794366715495587924829697045618064595517091398323127000591150167969423793125376862942962617933168868125721044755585292104012767604575090001864613992237960887242026855773279634028088706121371418922552125986506064146112561599205615974813154971272528592745144988174228621487749404677959591894452249599588096076892574585613962026186332366180174253118634077603697727952204486962202338916762987146793208323561031870496718547544796269555861921652')
```
Then we can get `p + q` through the formula mentioend above:
Then we can get $p + q$ through the formula mentioend above:
```py
>>> B = Decimal(N) - phi + 1
@ -101,7 +151,8 @@ Decimal('34642192582980793929380236893725052051755685627449634068179923908929124
>>> C = Decimal(N)
```
Check to make sure B and C are integers. If they're not, try using a higher precision in `getcontext().prec`. Now solve the quadratic equation:
Check to make sure $B$ and $C$ are integers. If they're not, try using a higher
precision in `getcontext().prec`. Now solve the quadratic equation:
```py
>>> p = (B + (B * B - 4 * C).sqrt()) / Decimal(2)
@ -112,13 +163,18 @@ Decimal('16823427526200025299629360726790945249096067335633200400252946099787748
True
```
We've successfully recovered `p` and `q` from just `N`, `e`, and `d`!
We've successfully recovered $p$ and $q$ from just $N$, $e$, and $d$!
### blinding
This attack is actually about RSA _signatures_ (which uses the opposite keys as encryption: private for signing and public for verifying), and shows how you can compute the signature of a message M using the signature of a derived message M'.
This attack is actually about RSA _signatures_ (which uses the opposite keys as
encryption: private for signing and public for verifying), and shows how you can
compute the signature of a message $M$ using the signature of a derived message
$M'$.
Suppose Marvin wants Bob to sign the following message: `"I (Bob) owes Marvin $100,000 USD"`. Marvin hands this to Bob saying something like, "I'll just need you to sign this with your private key." Let's generate Bob's private key:
Suppose Marvin wants Bob to sign the following message: `"I (Bob) owes Marvin
$100,000 USD"`. Marvin hands this to Bob saying something like, "I'll just need
you to sign this with your private key." Let's generate Bob's private key:
```py
>>> from Crypto.Util.number import bytes_to_long, long_to_bytes
@ -128,7 +184,10 @@ Suppose Marvin wants Bob to sign the following message: `"I (Bob) owes Marvin $1
>>> M = b"I (Bob) owes Marvin $100,000 USD"
```
Obviously, Bob, an intellectual, will refuse to sign the message. However, suppose Marvin now transforms his message into a more innocent looking one. He does this by turning M into `M' = (r^e)*M mod N` where r is an integer that's coprime to N:
Obviously, Bob, an intellectual, will refuse to sign the message. However,
suppose Marvin now transforms his message into a more innocent looking one. He
does this by turning $M$ into $M' = r^eM \mod N$ where r is an integer that's
coprime to $N$:
```py
>>> from random import randint
@ -138,21 +197,32 @@ Obviously, Bob, an intellectual, will refuse to sign the message. However, suppo
b'7\x90\xbc\xf9%T\xa9\xee\xf4\xe3?>]\x88\xcd\xb4\xd6D#\xfc\xcb\x0fd\xf0\x8e\xbc>\n\x06\xcd\x0f\x89\x0bp\xa7o\xd6\x02\xa6\xa7\x81\xd8\n\xae\xfb\x08\xaa|\xbd.\xc9E\xf1|\x86\xcaZ\xaa\xd4L\xafaA\x0c}\x84\x04\n\xa4\xa5\x80\xecX<\xe0\xb5\xf6\xfb\xe3\xcc\xd5BD7\xdc\xaep\x7f\xe9vi\xabB\xe2\xadE\xa41K\xc6\xb7\xae\x01\xcb\x04C\xaf\x8b\x17\x83\xffX7z\xb1\xbf\xceF\xafN(x\x00\x9f\xe1kV\xee\x0b\xbd\xc3H\r\xee9\x81\x16\xb2\x10hb.\x90\x08\xe42$Q\x92Ew+\xe1@\xf9\x17%\xce/\xbd\x00\xad\xe2\x12\x01\x93\x8b\xc4\x1bx\xe6H?\x15\xdfPE@\xf9j\xe3\xb7\x9e\xa0\x86\xd1\xd3\xb6[\xf7q\xf1\x95N\xd3>/\x06\x80\xc7\xa3\x8a\xcbDy\xc6v\x01P\x14\xa9Be\xf7~p\xc5\xaa\xac\xa0\xaf\xbe#\xe5\x18\xc6\x1d\xd5\x14\xc1\xbbYXD\x0c\x91{\xc0s\xde]\x18Z\x8bSk\x07k\xb6\x9a\xa5`Iqe~'
```
Now he asks Bob to sign this more... innocently-looking message. Without questioning, Bob, an intellectual, signs his life away. Let's say he produces a signature `S' = (M'^d) = (r^e * M)^d = r^(ed) * M^d = r * M^d mod N`.
Now he asks Bob to sign this more... innocently-looking message. Without
questioning, Bob, an intellectual, signs his life away. Let's say he produces a
signature
$$\begin{aligned}
S' &= (M'^d) \\\
&= (r^e * M)^d \\\
&= r^{ed} * M^d \\\
&= r * M^d \mod N
\end{aligned}$$
```py
>>> Sp, = bob.sign(Mp, 0)
4222298342813922437811434251340999736739055616654488323193778229765071846717137952694561809398626068283668428796351354154566771597532278827070832905206221261994843265685464173739776886856384806238418884247949451413559988796455422271296883338455956330421559319009950760931899199217936823999874162064553735563087382870564193673989865778229832918474778963380170967676966373703157629615331081637805594392084045827925764529711433584853942576464491576212176547485726609891593617931393545058401472883178443786988683045423150809606471425615670582973274971087459634959553685559458456237617436410759134193279063427911112115134
```
Now, all Marvin has to do is multiply by the modular inverse of r, to obtain `M^d`, the signature of the original message:
Now, all Marvin has to do is multiply by the modular inverse of $r$, to obtain
$M^d$, the signature of the original message:
```py
>>> S = (Sp * modinv(r, N)) % N
6137678992536399703654836416525985142902780822513172949427421060785532284955531529418529725602418902796840570634560123808769013384654624916503940938715718120521434666716675795201896105310462331838807171312705686415521871046533303776516500490921892398440988515777575520183847518597482163414665355222659603386541869176930658730416118799866012276767364050134126722746224706026850062367243018313483359694686773566231956425606553198607719740067340776177716443517567144901614253170719278035838849363127850910135864099535083004590180745762100334268408681888925040382341592080592207557742366581814701422371311084081150092871
```
Sure enough, if you try to verify the "original" signature against the original message, it checks out.
Sure enough, if you try to verify the "original" signature against the original
message, it checks out.
```py
>>> bob.verify(M, (S,))

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+++
title = "The Cyber Grabs CTF: Unbr34k4bl3 (942)"
draft = true
date = 2022-02-02
tags = ["ctf", "crypto"]
languages = ["python"]
layout = "single"
math = true
+++
Crypto challenge Unbr34k4bl3 from the Cyber Grabs CTF.
<!--more-->
> No one can break my rsa encryption, prove me wrong !!
>
> Flag Format: cybergrabs{}
>
> Author: Mritunjya
>
> [output.txt] [source.py]
[output.txt]: ./output.txt
[source.py]: ./source.py
Looking at the source code, this challenge looks like a typical RSA challenge at
first, but there are some important differences to note:
- $N = pqr$ (line 34). This is a twist but RSA strategies can easily be
extended to 3 prime components.
- $p, q \equiv 3 \mod 4$ (line 19). This suggests that the cryptosystem is
actually a [Rabin cryptosystem][Rabin].
- We're not given the public keys $e_1$ and $e_2$, but they are related through
$x$.
[Rabin]: https://en.wikipedia.org/wiki/Rabin_cryptosystem
## Finding $e_1$ and $e_2$
We know that $e_1$ and $e_2$ are related through $x$, which is some even number
greater than 2, but we're not given any of their real values. We're also given
through an oddly-named `functor` function that:
$$
\begin{aligned}
1 + e_1 + e_1^2 + \cdots + e_1^x &= 1 + e_2 + e_2^2 \\\
\frac{1 - e_1^x}{1 - e_1} &= 1 + e_2 + e_2^2
\end{aligned}
$$
Interestingly enough, since $e_1$ and $e_2$ are primes, that means
I'd like to thank @10, @sahuang, and @thebishop in the Project Sekai discord for
their help throughout this challenge.

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@ -0,0 +1,5 @@
n:267362205744654830055585746250317245125479735269853713372687604676608285629127977574310510441358104169652444917329986129098240750401425257601282268733834091593200445244725460613298199140690597119199763970064359847666802255456013592631532853951273286284878230893809080250386646832110506402289378691079462364884899662707502858007857457806853302449695351229004051902617728418480990341155900565542195318206284041182555579388392863474548687784403795738945489219689610881075059037192656116884269582257788959555951074322245033492165406470004019896763472332962300128378758934128374039937693688718317737657946435827745981009467876838127075176808098467305627394472135213533754815713468369763665632168616054982745256773112537152292099369137072982289095951236065885648588670059655452986720063260146952425798150221407866669449837430999779776718047668562687216933053536759554900663226163021145439386115076821161003965334731127329486856711654741683760749336235855319144478194501034662638054193682000283319917096796971
ip:65491313526527942082900846848440586365393305192439699810712229312474732937502934334921061033822729150056656630858908294464249602368303871630644420585085642204592189073314730233318796675949142968346807766087775542461078648703191450221286915401606901781524237580646760734493950360267230729125514156671619347616
iq:97034409222811998555255396847918439343239825222504093225438959283117395075159811973044380473862026342866489725039905931430797650466599952795602909181290621103197493223080488468216279214006070950393096075839913101687588555346523517436421698916141195686143520143972735534402754157166545851899187305574703394138
c1:103687839591259628532585171241634220321003599759860095236990117623065664975385083122971507015385215246948744078816596026772744294701233346732383214113445480056584639282712898073542520168025667980980057512174927564196375256682206601425714094930670415979638437119896258396784978194294581076901000507291277729888015413204446158926865037965291316577726275211006619643531704449499845352147547986667837681877488120093302675775792115380914560935989896453159186176952126083066619414338359303033325593504442257083571002878083287293828310810483726711816109297046925744157605591270761804522735216774801135342322479770391505911100485259078064775709124730966391629468398187269096529671187877954443617005248499140455160589093379715757808387108825458007733207099871941497372539249357162437077379731766825184301649010270921003130776410066972952756983157217280397531412843118202051922048479332111760976091302376602674590153876045380552746826056547929265785960676415919260117136285580971488670143947003566230254837742519
c2:171159809874438596904787534111610260851529969068192878049771299710688449419966698428704180474774734112617652498954998301185232279153644173070897800123538474930545720934844727376637921072749901149514789723141795042182408704214998390482343965532559149095934231081729041402598776401575561653660624208366051273601230345754361771067242657825194926706328336322383296953817730346429591680463526267530372572332663327157636745578067246913529155120642276894180354494816411827468256127607558873938451944866168777913756913920336763454881108023708284527878322162463081091624350220308273550298342755582044860337692076513609120342318151660103532559583052954725303030103413034880155621982581677423267299780543045375467310718078800411397780269409147558121862038983169509828944551199620508493589091401498720419409158373805529997911655270528589050795214164221299581104149954423726171539700223299445034347915430838395255700425648686205603925507474877720680274914513203566997846945579395522000899007446797091893230195801607

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@ -0,0 +1,53 @@
from Crypto.Util.number import *
from secret import *
assert (x>2 and x%2 == 0)
assert (isPrime(e1) and isPrime(e2))
def functor():
val1 , val2 = 0,0
for i in range(x+1):
val1 += pow(e1,i)
for j in range(3):
val2 += pow(e2,j)
assert (val1 == val2)
def keygen():
while True:
p,q = [getStrongPrime(1024) for _ in range(2)]
if p%4==3 and q%4==3:
break
r = 2
while True:
r = r*x
if r.bit_length()>1024 and isPrime(r-1):
r = r-1
break
return p,q,r
functor()
p,q,r = keygen()
n = p*q*r
print(f"p:{p}")
print(f"q:{q}")
ip = inverse(p,q)
iq = inverse(q,p)
c1 = pow(bytes_to_long(flag[0:len(flag)//2].encode('utf-8')),e1,n)
c2 = pow(bytes_to_long(flag[len(flag)//2:].encode('utf-8')),e2,n)
print(f"n:{n}",f"ip:{ip}",f"iq:{iq}",f"c1:{c1}",f"c2:{c2}",sep="\n")

1
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@ -6,6 +6,7 @@
<title>michael's blog</title>
{{ block "headExtra" . }}{{ end }}
{{ partial "head" . }}
{{ $style := resources.Get "sass/main.scss" | resources.ToCSS }}
<link rel="stylesheet" href="{{ $style.RelPermalink }}" />

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{{ if .Params.math }}{{ partial "katex.html" . }}{{ end }}

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<link rel="stylesheet" href="/katex/katex.min.css">
<script defer src="/katex/katex.min.js"></script>
<script defer src="/katex/contrib/auto-render.min.js" onload="renderMathInElement(document.body);"></script>
<script>
document.addEventListener("DOMContentLoaded", function() {
renderMathInElement(document.body, {
// customised options
// • auto-render specific keys, e.g.:
delimiters: [
{left: '$$', right: '$$', display: true},
{left: '$', right: '$', display: false},
{left: '\\(', right: '\\)', display: false},
{left: '\\[', right: '\\]', display: true}
],
// • rendering keys, e.g.:
throwOnError : false
});
});
</script>

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# [<img src="https://katex.org/img/katex-logo-black.svg" width="130" alt="KaTeX">](https://katex.org/)
[![npm](https://img.shields.io/npm/v/katex.svg)](https://www.npmjs.com/package/katex)
[![semantic-release](https://img.shields.io/badge/%20%20%F0%9F%93%A6%F0%9F%9A%80-semantic--release-e10079.svg)](https://github.com/semantic-release/semantic-release)
[![CI](https://github.com/KaTeX/KaTeX/workflows/CI/badge.svg?branch=main&event=push)](https://github.com/KaTeX/KaTeX/actions?query=workflow%3ACI)
[![codecov](https://codecov.io/gh/KaTeX/KaTeX/branch/main/graph/badge.svg)](https://codecov.io/gh/KaTeX/KaTeX)
[![Discussions](https://img.shields.io/badge/Discussions-join-brightgreen)](https://github.com/KaTeX/KaTeX/discussions)
[![jsDelivr](https://data.jsdelivr.com/v1/package/npm/katex/badge?style=rounded)](https://www.jsdelivr.com/package/npm/katex)
![katex.min.js size](https://img.badgesize.io/https://unpkg.com/katex/dist/katex.min.js?compression=gzip)
[![Gitpod ready-to-code](https://img.shields.io/badge/Gitpod-ready--to--code-blue?logo=gitpod)](https://gitpod.io/#https://github.com/KaTeX/KaTeX)
[![Financial Contributors on Open Collective](https://opencollective.com/katex/all/badge.svg?label=financial+contributors)](https://opencollective.com/katex)
KaTeX is a fast, easy-to-use JavaScript library for TeX math rendering on the web.
* **Fast:** KaTeX renders its math synchronously and doesn't need to reflow the page. See how it compares to a competitor in [this speed test](http://www.intmath.com/cg5/katex-mathjax-comparison.php).
* **Print quality:** KaTeX's layout is based on Donald Knuth's TeX, the gold standard for math typesetting.
* **Self contained:** KaTeX has no dependencies and can easily be bundled with your website resources.
* **Server side rendering:** KaTeX produces the same output regardless of browser or environment, so you can pre-render expressions using Node.js and send them as plain HTML.
KaTeX is compatible with all major browsers, including Chrome, Safari, Firefox, Opera, Edge, and IE 11.
KaTeX supports much (but not all) of LaTeX and many LaTeX packages. See the [list of supported functions](https://katex.org/docs/supported.html).
Try out KaTeX [on the demo page](https://katex.org/#demo)!
## Getting started
### Starter template
```html
<!DOCTYPE html>
<!-- KaTeX requires the use of the HTML5 doctype. Without it, KaTeX may not render properly -->
<html>
<head>
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/katex@0.15.2/dist/katex.min.css" integrity="sha384-MlJdn/WNKDGXveldHDdyRP1R4CTHr3FeuDNfhsLPYrq2t0UBkUdK2jyTnXPEK1NQ" crossorigin="anonymous">
<!-- The loading of KaTeX is deferred to speed up page rendering -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.15.2/dist/katex.min.js" integrity="sha384-VQ8d8WVFw0yHhCk5E8I86oOhv48xLpnDZx5T9GogA/Y84DcCKWXDmSDfn13bzFZY" crossorigin="anonymous"></script>
<!-- To automatically render math in text elements, include the auto-render extension: -->
<script defer src="https://cdn.jsdelivr.net/npm/katex@0.15.2/dist/contrib/auto-render.min.js" integrity="sha384-+XBljXPPiv+OzfbB3cVmLHf4hdUFHlWNZN5spNQ7rmHTXpd7WvJum6fIACpNNfIR" crossorigin="anonymous"
onload="renderMathInElement(document.body);"></script>
</head>
...
</html>
```
You can also [download KaTeX](https://github.com/KaTeX/KaTeX/releases) and host it yourself.
For details on how to configure auto-render extension, refer to [the documentation](https://katex.org/docs/autorender.html).
### API
Call `katex.render` to render a TeX expression directly into a DOM element.
For example:
```js
katex.render("c = \\pm\\sqrt{a^2 + b^2}", element, {
throwOnError: false
});
```
Call `katex.renderToString` to generate an HTML string of the rendered math,
e.g., for server-side rendering. For example:
```js
var html = katex.renderToString("c = \\pm\\sqrt{a^2 + b^2}", {
throwOnError: false
});
// '<span class="katex">...</span>'
```
Make sure to include the CSS and font files in both cases.
If you are doing all rendering on the server, there is no need to include the
JavaScript on the client.
The examples above use the `throwOnError: false` option, which renders invalid
inputs as the TeX source code in red (by default), with the error message as
hover text. For other available options, see the
[API documentation](https://katex.org/docs/api.html),
[options documentation](https://katex.org/docs/options.html), and
[handling errors documentation](https://katex.org/docs/error.html).
## Demo and Documentation
Learn more about using KaTeX [on the website](https://katex.org)!
## Contributors
### Code Contributors
This project exists thanks to all the people who contribute code. If you'd like to help, see [our guide to contributing code](CONTRIBUTING.md).
<a href="https://github.com/KaTeX/KaTeX/graphs/contributors"><img src="https://contributors-svg.opencollective.com/katex/contributors.svg?width=890&button=false" alt="Code contributors" /></a>
### Financial Contributors
Become a financial contributor and help us sustain our community.
#### Individuals
<a href="https://opencollective.com/katex"><img src="https://opencollective.com/katex/individuals.svg?width=890" alt="Contribute on Open Collective"></a>
#### Organizations
Support this project with your organization. Your logo will show up here with a link to your website.
<a href="https://opencollective.com/katex/organization/0/website"><img src="https://opencollective.com/katex/organization/0/avatar.svg" alt="Organization 1"></a>
<a href="https://opencollective.com/katex/organization/1/website"><img src="https://opencollective.com/katex/organization/1/avatar.svg" alt="Organization 2"></a>
<a href="https://opencollective.com/katex/organization/2/website"><img src="https://opencollective.com/katex/organization/2/avatar.svg" alt="Organization 3"></a>
<a href="https://opencollective.com/katex/organization/3/website"><img src="https://opencollective.com/katex/organization/3/avatar.svg" alt="Organization 4"></a>
<a href="https://opencollective.com/katex/organization/4/website"><img src="https://opencollective.com/katex/organization/4/avatar.svg" alt="Organization 5"></a>
<a href="https://opencollective.com/katex/organization/5/website"><img src="https://opencollective.com/katex/organization/5/avatar.svg" alt="Organization 6"></a>
<a href="https://opencollective.com/katex/organization/6/website"><img src="https://opencollective.com/katex/organization/6/avatar.svg" alt="Organization 7"></a>
<a href="https://opencollective.com/katex/organization/7/website"><img src="https://opencollective.com/katex/organization/7/avatar.svg" alt="Organization 8"></a>
<a href="https://opencollective.com/katex/organization/8/website"><img src="https://opencollective.com/katex/organization/8/avatar.svg" alt="Organization 9"></a>
<a href="https://opencollective.com/katex/organization/9/website"><img src="https://opencollective.com/katex/organization/9/avatar.svg" alt="Organization 10"></a>
## License
KaTeX is licensed under the [MIT License](http://opensource.org/licenses/MIT).

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(function webpackUniversalModuleDefinition(root, factory) {
if(typeof exports === 'object' && typeof module === 'object')
module.exports = factory(require("katex"));
else if(typeof define === 'function' && define.amd)
define(["katex"], factory);
else if(typeof exports === 'object')
exports["renderMathInElement"] = factory(require("katex"));
else
root["renderMathInElement"] = factory(root["katex"]);
})((typeof self !== 'undefined' ? self : this), function(__WEBPACK_EXTERNAL_MODULE__771__) {
return /******/ (function() { // webpackBootstrap
/******/ "use strict";
/******/ var __webpack_modules__ = ({
/***/ 771:
/***/ (function(module) {
module.exports = __WEBPACK_EXTERNAL_MODULE__771__;
/***/ })
/******/ });
/************************************************************************/
/******/ // The module cache
/******/ var __webpack_module_cache__ = {};
/******/
/******/ // The require function
/******/ function __webpack_require__(moduleId) {
/******/ // Check if module is in cache
/******/ var cachedModule = __webpack_module_cache__[moduleId];
/******/ if (cachedModule !== undefined) {
/******/ return cachedModule.exports;
/******/ }
/******/ // Create a new module (and put it into the cache)
/******/ var module = __webpack_module_cache__[moduleId] = {
/******/ // no module.id needed
/******/ // no module.loaded needed
/******/ exports: {}
/******/ };
/******/
/******/ // Execute the module function
/******/ __webpack_modules__[moduleId](module, module.exports, __webpack_require__);
/******/
/******/ // Return the exports of the module
/******/ return module.exports;
/******/ }
/******/
/************************************************************************/
/******/ /* webpack/runtime/compat get default export */
/******/ !function() {
/******/ // getDefaultExport function for compatibility with non-harmony modules
/******/ __webpack_require__.n = function(module) {
/******/ var getter = module && module.__esModule ?
/******/ function() { return module['default']; } :
/******/ function() { return module; };
/******/ __webpack_require__.d(getter, { a: getter });
/******/ return getter;
/******/ };
/******/ }();
/******/
/******/ /* webpack/runtime/define property getters */
/******/ !function() {
/******/ // define getter functions for harmony exports
/******/ __webpack_require__.d = function(exports, definition) {
/******/ for(var key in definition) {
/******/ if(__webpack_require__.o(definition, key) && !__webpack_require__.o(exports, key)) {
/******/ Object.defineProperty(exports, key, { enumerable: true, get: definition[key] });
/******/ }
/******/ }
/******/ };
/******/ }();
/******/
/******/ /* webpack/runtime/hasOwnProperty shorthand */
/******/ !function() {
/******/ __webpack_require__.o = function(obj, prop) { return Object.prototype.hasOwnProperty.call(obj, prop); }
/******/ }();
/******/
/************************************************************************/
var __webpack_exports__ = {};
// This entry need to be wrapped in an IIFE because it need to be isolated against other modules in the chunk.
!function() {
// EXPORTS
__webpack_require__.d(__webpack_exports__, {
"default": function() { return /* binding */ auto_render; }
});
// EXTERNAL MODULE: external "katex"
var external_katex_ = __webpack_require__(771);
var external_katex_default = /*#__PURE__*/__webpack_require__.n(external_katex_);
;// CONCATENATED MODULE: ./contrib/auto-render/splitAtDelimiters.js
/* eslint no-constant-condition:0 */
var findEndOfMath = function findEndOfMath(delimiter, text, startIndex) {
// Adapted from
// https://github.com/Khan/perseus/blob/master/src/perseus-markdown.jsx
var index = startIndex;
var braceLevel = 0;
var delimLength = delimiter.length;
while (index < text.length) {
var character = text[index];
if (braceLevel <= 0 && text.slice(index, index + delimLength) === delimiter) {
return index;
} else if (character === "\\") {
index++;
} else if (character === "{") {
braceLevel++;
} else if (character === "}") {
braceLevel--;
}
index++;
}
return -1;
};
var escapeRegex = function escapeRegex(string) {
return string.replace(/[-/\\^$*+?.()|[\]{}]/g, "\\$&");
};
var amsRegex = /^\\begin{/;
var splitAtDelimiters = function splitAtDelimiters(text, delimiters) {
var index;
var data = [];
var regexLeft = new RegExp("(" + delimiters.map(function (x) {
return escapeRegex(x.left);
}).join("|") + ")");
while (true) {
index = text.search(regexLeft);
if (index === -1) {
break;
}
if (index > 0) {
data.push({
type: "text",
data: text.slice(0, index)
});
text = text.slice(index); // now text starts with delimiter
} // ... so this always succeeds:
var i = delimiters.findIndex(function (delim) {
return text.startsWith(delim.left);
});
index = findEndOfMath(delimiters[i].right, text, delimiters[i].left.length);
if (index === -1) {
break;
}
var rawData = text.slice(0, index + delimiters[i].right.length);
var math = amsRegex.test(rawData) ? rawData : text.slice(delimiters[i].left.length, index);
data.push({
type: "math",
data: math,
rawData: rawData,
display: delimiters[i].display
});
text = text.slice(index + delimiters[i].right.length);
}
if (text !== "") {
data.push({
type: "text",
data: text
});
}
return data;
};
/* harmony default export */ var auto_render_splitAtDelimiters = (splitAtDelimiters);
;// CONCATENATED MODULE: ./contrib/auto-render/auto-render.js
/* eslint no-console:0 */
/* Note: optionsCopy is mutated by this method. If it is ever exposed in the
* API, we should copy it before mutating.
*/
var renderMathInText = function renderMathInText(text, optionsCopy) {
var data = auto_render_splitAtDelimiters(text, optionsCopy.delimiters);
if (data.length === 1 && data[0].type === 'text') {
// There is no formula in the text.
// Let's return null which means there is no need to replace
// the current text node with a new one.
return null;
}
var fragment = document.createDocumentFragment();
for (var i = 0; i < data.length; i++) {
if (data[i].type === "text") {
fragment.appendChild(document.createTextNode(data[i].data));
} else {
var span = document.createElement("span");
var math = data[i].data; // Override any display mode defined in the settings with that
// defined by the text itself
optionsCopy.displayMode = data[i].display;
try {
if (optionsCopy.preProcess) {
math = optionsCopy.preProcess(math);
}
external_katex_default().render(math, span, optionsCopy);
} catch (e) {
if (!(e instanceof (external_katex_default()).ParseError)) {
throw e;
}
optionsCopy.errorCallback("KaTeX auto-render: Failed to parse `" + data[i].data + "` with ", e);
fragment.appendChild(document.createTextNode(data[i].rawData));
continue;
}
fragment.appendChild(span);
}
}
return fragment;
};
var renderElem = function renderElem(elem, optionsCopy) {
for (var i = 0; i < elem.childNodes.length; i++) {
var childNode = elem.childNodes[i];
if (childNode.nodeType === 3) {
// Text node
var frag = renderMathInText(childNode.textContent, optionsCopy);
if (frag) {
i += frag.childNodes.length - 1;
elem.replaceChild(frag, childNode);
}
} else if (childNode.nodeType === 1) {
(function () {
// Element node
var className = ' ' + childNode.className + ' ';
var shouldRender = optionsCopy.ignoredTags.indexOf(childNode.nodeName.toLowerCase()) === -1 && optionsCopy.ignoredClasses.every(function (x) {
return className.indexOf(' ' + x + ' ') === -1;
});
if (shouldRender) {
renderElem(childNode, optionsCopy);
}
})();
} // Otherwise, it's something else, and ignore it.
}
};
var renderMathInElement = function renderMathInElement(elem, options) {
if (!elem) {
throw new Error("No element provided to render");
}
var optionsCopy = {}; // Object.assign(optionsCopy, option)
for (var option in options) {
if (options.hasOwnProperty(option)) {
optionsCopy[option] = options[option];
}
} // default options
optionsCopy.delimiters = optionsCopy.delimiters || [{
left: "$$",
right: "$$",
display: true
}, {
left: "\\(",
right: "\\)",
display: false
}, // LaTeX uses $…$, but it ruins the display of normal `$` in text:
// {left: "$", right: "$", display: false},
// $ must come after $$
// Render AMS environments even if outside $$…$$ delimiters.
{
left: "\\begin{equation}",
right: "\\end{equation}",
display: true
}, {
left: "\\begin{align}",
right: "\\end{align}",
display: true
}, {
left: "\\begin{alignat}",
right: "\\end{alignat}",
display: true
}, {
left: "\\begin{gather}",
right: "\\end{gather}",
display: true
}, {
left: "\\begin{CD}",
right: "\\end{CD}",
display: true
}, {
left: "\\[",
right: "\\]",
display: true
}];
optionsCopy.ignoredTags = optionsCopy.ignoredTags || ["script", "noscript", "style", "textarea", "pre", "code", "option"];
optionsCopy.ignoredClasses = optionsCopy.ignoredClasses || [];
optionsCopy.errorCallback = optionsCopy.errorCallback || console.error; // Enable sharing of global macros defined via `\gdef` between different
// math elements within a single call to `renderMathInElement`.
optionsCopy.macros = optionsCopy.macros || {};
renderElem(elem, optionsCopy);
};
/* harmony default export */ var auto_render = (renderMathInElement);
}();
__webpack_exports__ = __webpack_exports__["default"];
/******/ return __webpack_exports__;
/******/ })()
;
});

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!function(e,t){"object"==typeof exports&&"object"==typeof module?module.exports=t(require("katex")):"function"==typeof define&&define.amd?define(["katex"],t):"object"==typeof exports?exports.renderMathInElement=t(require("katex")):e.renderMathInElement=t(e.katex)}("undefined"!=typeof self?self:this,(function(e){return function(){"use strict";var t={771:function(t){t.exports=e}},r={};function n(e){var a=r[e];if(void 0!==a)return a.exports;var i=r[e]={exports:{}};return t[e](i,i.exports,n),i.exports}n.n=function(e){var t=e&&e.__esModule?function(){return e.default}:function(){return e};return n.d(t,{a:t}),t},n.d=function(e,t){for(var r in t)n.o(t,r)&&!n.o(e,r)&&Object.defineProperty(e,r,{enumerable:!0,get:t[r]})},n.o=function(e,t){return Object.prototype.hasOwnProperty.call(e,t)};var a={};return function(){n.d(a,{default:function(){return s}});var e=n(771),t=n.n(e),r=function(e,t,r){for(var n=r,a=0,i=e.length;n<t.length;){var o=t[n];if(a<=0&&t.slice(n,n+i)===e)return n;"\\"===o?n++:"{"===o?a++:"}"===o&&a--,n++}return-1},i=/^\\begin{/,o=function(e,t){for(var n,a=[],o=new RegExp("("+t.map((function(e){return e.left.replace(/[-/\\^$*+?.()|[\]{}]/g,"\\$&")})).join("|")+")");-1!==(n=e.search(o));){n>0&&(a.push({type:"text",data:e.slice(0,n)}),e=e.slice(n));var l=t.findIndex((function(t){return e.startsWith(t.left)}));if(-1===(n=r(t[l].right,e,t[l].left.length)))break;var d=e.slice(0,n+t[l].right.length),s=i.test(d)?d:e.slice(t[l].left.length,n);a.push({type:"math",data:s,rawData:d,display:t[l].display}),e=e.slice(n+t[l].right.length)}return""!==e&&a.push({type:"text",data:e}),a},l=function(e,r){var n=o(e,r.delimiters);if(1===n.length&&"text"===n[0].type)return null;for(var a=document.createDocumentFragment(),i=0;i<n.length;i++)if("text"===n[i].type)a.appendChild(document.createTextNode(n[i].data));else{var l=document.createElement("span"),d=n[i].data;r.displayMode=n[i].display;try{r.preProcess&&(d=r.preProcess(d)),t().render(d,l,r)}catch(e){if(!(e instanceof t().ParseError))throw e;r.errorCallback("KaTeX auto-render: Failed to parse `"+n[i].data+"` with ",e),a.appendChild(document.createTextNode(n[i].rawData));continue}a.appendChild(l)}return a},d=function e(t,r){for(var n=0;n<t.childNodes.length;n++){var a=t.childNodes[n];if(3===a.nodeType){var i=l(a.textContent,r);i&&(n+=i.childNodes.length-1,t.replaceChild(i,a))}else 1===a.nodeType&&function(){var t=" "+a.className+" ";-1===r.ignoredTags.indexOf(a.nodeName.toLowerCase())&&r.ignoredClasses.every((function(e){return-1===t.indexOf(" "+e+" ")}))&&e(a,r)}()}},s=function(e,t){if(!e)throw new Error("No element provided to render");var r={};for(var n in t)t.hasOwnProperty(n)&&(r[n]=t[n]);r.delimiters=r.delimiters||[{left:"$$",right:"$$",display:!0},{left:"\\(",right:"\\)",display:!1},{left:"\\begin{equation}",right:"\\end{equation}",display:!0},{left:"\\begin{align}",right:"\\end{align}",display:!0},{left:"\\begin{alignat}",right:"\\end{alignat}",display:!0},{left:"\\begin{gather}",right:"\\end{gather}",display:!0},{left:"\\begin{CD}",right:"\\end{CD}",display:!0},{left:"\\[",right:"\\]",display:!0}],r.ignoredTags=r.ignoredTags||["script","noscript","style","textarea","pre","code","option"],r.ignoredClasses=r.ignoredClasses||[],r.errorCallback=r.errorCallback||console.error,r.macros=r.macros||{},d(e,r)}}(),a=a.default}()}));

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import katex from '../katex.mjs';
/* eslint no-constant-condition:0 */
var findEndOfMath = function findEndOfMath(delimiter, text, startIndex) {
// Adapted from
// https://github.com/Khan/perseus/blob/master/src/perseus-markdown.jsx
var index = startIndex;
var braceLevel = 0;
var delimLength = delimiter.length;
while (index < text.length) {
var character = text[index];
if (braceLevel <= 0 && text.slice(index, index + delimLength) === delimiter) {
return index;
} else if (character === "\\") {
index++;
} else if (character === "{") {
braceLevel++;
} else if (character === "}") {
braceLevel--;
}
index++;
}
return -1;
};
var escapeRegex = function escapeRegex(string) {
return string.replace(/[-/\\^$*+?.()|[\]{}]/g, "\\$&");
};
var amsRegex = /^\\begin{/;
var splitAtDelimiters = function splitAtDelimiters(text, delimiters) {
var index;
var data = [];
var regexLeft = new RegExp("(" + delimiters.map(x => escapeRegex(x.left)).join("|") + ")");
while (true) {
index = text.search(regexLeft);
if (index === -1) {
break;
}
if (index > 0) {
data.push({
type: "text",
data: text.slice(0, index)
});
text = text.slice(index); // now text starts with delimiter
} // ... so this always succeeds:
var i = delimiters.findIndex(delim => text.startsWith(delim.left));
index = findEndOfMath(delimiters[i].right, text, delimiters[i].left.length);
if (index === -1) {
break;
}
var rawData = text.slice(0, index + delimiters[i].right.length);
var math = amsRegex.test(rawData) ? rawData : text.slice(delimiters[i].left.length, index);
data.push({
type: "math",
data: math,
rawData,
display: delimiters[i].display
});
text = text.slice(index + delimiters[i].right.length);
}
if (text !== "") {
data.push({
type: "text",
data: text
});
}
return data;
};
/* eslint no-console:0 */
/* Note: optionsCopy is mutated by this method. If it is ever exposed in the
* API, we should copy it before mutating.
*/
var renderMathInText = function renderMathInText(text, optionsCopy) {
var data = splitAtDelimiters(text, optionsCopy.delimiters);
if (data.length === 1 && data[0].type === 'text') {
// There is no formula in the text.
// Let's return null which means there is no need to replace
// the current text node with a new one.
return null;
}
var fragment = document.createDocumentFragment();
for (var i = 0; i < data.length; i++) {
if (data[i].type === "text") {
fragment.appendChild(document.createTextNode(data[i].data));
} else {
var span = document.createElement("span");
var math = data[i].data; // Override any display mode defined in the settings with that
// defined by the text itself
optionsCopy.displayMode = data[i].display;
try {
if (optionsCopy.preProcess) {
math = optionsCopy.preProcess(math);
}
katex.render(math, span, optionsCopy);
} catch (e) {
if (!(e instanceof katex.ParseError)) {
throw e;
}
optionsCopy.errorCallback("KaTeX auto-render: Failed to parse `" + data[i].data + "` with ", e);
fragment.appendChild(document.createTextNode(data[i].rawData));
continue;
}
fragment.appendChild(span);
}
}
return fragment;
};
var renderElem = function renderElem(elem, optionsCopy) {
for (var i = 0; i < elem.childNodes.length; i++) {
var childNode = elem.childNodes[i];
if (childNode.nodeType === 3) {
// Text node
var frag = renderMathInText(childNode.textContent, optionsCopy);
if (frag) {
i += frag.childNodes.length - 1;
elem.replaceChild(frag, childNode);
}
} else if (childNode.nodeType === 1) {
(function () {
// Element node
var className = ' ' + childNode.className + ' ';
var shouldRender = optionsCopy.ignoredTags.indexOf(childNode.nodeName.toLowerCase()) === -1 && optionsCopy.ignoredClasses.every(x => className.indexOf(' ' + x + ' ') === -1);
if (shouldRender) {
renderElem(childNode, optionsCopy);
}
})();
} // Otherwise, it's something else, and ignore it.
}
};
var renderMathInElement = function renderMathInElement(elem, options) {
if (!elem) {
throw new Error("No element provided to render");
}
var optionsCopy = {}; // Object.assign(optionsCopy, option)
for (var option in options) {
if (options.hasOwnProperty(option)) {
optionsCopy[option] = options[option];
}
} // default options
optionsCopy.delimiters = optionsCopy.delimiters || [{
left: "$$",
right: "$$",
display: true
}, {
left: "\\(",
right: "\\)",
display: false
}, // LaTeX uses $…$, but it ruins the display of normal `$` in text:
// {left: "$", right: "$", display: false},
// $ must come after $$
// Render AMS environments even if outside $$…$$ delimiters.
{
left: "\\begin{equation}",
right: "\\end{equation}",
display: true
}, {
left: "\\begin{align}",
right: "\\end{align}",
display: true
}, {
left: "\\begin{alignat}",
right: "\\end{alignat}",
display: true
}, {
left: "\\begin{gather}",
right: "\\end{gather}",
display: true
}, {
left: "\\begin{CD}",
right: "\\end{CD}",
display: true
}, {
left: "\\[",
right: "\\]",
display: true
}];
optionsCopy.ignoredTags = optionsCopy.ignoredTags || ["script", "noscript", "style", "textarea", "pre", "code", "option"];
optionsCopy.ignoredClasses = optionsCopy.ignoredClasses || [];
optionsCopy.errorCallback = optionsCopy.errorCallback || console.error; // Enable sharing of global macros defined via `\gdef` between different
// math elements within a single call to `renderMathInElement`.
optionsCopy.macros = optionsCopy.macros || {};
renderElem(elem, optionsCopy);
};
export { renderMathInElement as default };

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/* Force selection of entire .katex/.katex-display blocks, so that we can
* copy/paste the entire source code. If you omit this CSS, partial
* selections of a formula will work, but will copy the ugly HTML
* representation instead of the LaTeX source code. (Full selections will
* still produce the LaTeX source code.)
*/
.katex,
.katex-display {
-webkit-user-select: all;
-moz-user-select: all;
-ms-user-select: all;
user-select: all;
}

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(function webpackUniversalModuleDefinition(root, factory) {
if(typeof exports === 'object' && typeof module === 'object')
module.exports = factory();
else if(typeof define === 'function' && define.amd)
define([], factory);
else {
var a = factory();
for(var i in a) (typeof exports === 'object' ? exports : root)[i] = a[i];
}
})((typeof self !== 'undefined' ? self : this), function() {
return /******/ (function() { // webpackBootstrap
/******/ "use strict";
var __webpack_exports__ = {};
;// CONCATENATED MODULE: ./contrib/copy-tex/katex2tex.js
// Set these to how you want inline and display math to be delimited.
var defaultCopyDelimiters = {
inline: ['$', '$'],
// alternative: ['\(', '\)']
display: ['$$', '$$'] // alternative: ['\[', '\]']
}; // Replace .katex elements with their TeX source (<annotation> element).
// Modifies fragment in-place. Useful for writing your own 'copy' handler,
// as in copy-tex.js.
var katexReplaceWithTex = function katexReplaceWithTex(fragment, copyDelimiters) {
if (copyDelimiters === void 0) {
copyDelimiters = defaultCopyDelimiters;
}
// Remove .katex-html blocks that are preceded by .katex-mathml blocks
// (which will get replaced below).
var katexHtml = fragment.querySelectorAll('.katex-mathml + .katex-html');
for (var i = 0; i < katexHtml.length; i++) {
var element = katexHtml[i];
if (element.remove) {
element.remove(null);
} else {
element.parentNode.removeChild(element);
}
} // Replace .katex-mathml elements with their annotation (TeX source)
// descendant, with inline delimiters.
var katexMathml = fragment.querySelectorAll('.katex-mathml');
for (var _i = 0; _i < katexMathml.length; _i++) {
var _element = katexMathml[_i];
var texSource = _element.querySelector('annotation');
if (texSource) {
if (_element.replaceWith) {
_element.replaceWith(texSource);
} else {
_element.parentNode.replaceChild(texSource, _element);
}
texSource.innerHTML = copyDelimiters.inline[0] + texSource.innerHTML + copyDelimiters.inline[1];
}
} // Switch display math to display delimiters.
var displays = fragment.querySelectorAll('.katex-display annotation');
for (var _i2 = 0; _i2 < displays.length; _i2++) {
var _element2 = displays[_i2];
_element2.innerHTML = copyDelimiters.display[0] + _element2.innerHTML.substr(copyDelimiters.inline[0].length, _element2.innerHTML.length - copyDelimiters.inline[0].length - copyDelimiters.inline[1].length) + copyDelimiters.display[1];
}
return fragment;
};
/* harmony default export */ var katex2tex = (katexReplaceWithTex);
;// CONCATENATED MODULE: ./contrib/copy-tex/copy-tex.js
// Global copy handler to modify behavior on .katex elements.
document.addEventListener('copy', function (event) {
var selection = window.getSelection();
if (selection.isCollapsed) {
return; // default action OK if selection is empty
}
var fragment = selection.getRangeAt(0).cloneContents();
if (!fragment.querySelector('.katex-mathml')) {
return; // default action OK if no .katex-mathml elements
} // Preserve usual HTML copy/paste behavior.
var html = [];
for (var i = 0; i < fragment.childNodes.length; i++) {
html.push(fragment.childNodes[i].outerHTML);
}
event.clipboardData.setData('text/html', html.join('')); // Rewrite plain-text version.
event.clipboardData.setData('text/plain', katex2tex(fragment).textContent); // Prevent normal copy handling.
event.preventDefault();
});
;// CONCATENATED MODULE: ./contrib/copy-tex/copy-tex.webpack.js
/**
* This is the webpack entry point for KaTeX. As ECMAScript doesn't support
* CSS modules natively, a separate entry point is used.
*/
__webpack_exports__ = __webpack_exports__["default"];
/******/ return __webpack_exports__;
/******/ })()
;
});

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.katex,.katex-display{-webkit-user-select:all;-moz-user-select:all;-ms-user-select:all;user-select:all}

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!function(e,t){if("object"==typeof exports&&"object"==typeof module)module.exports=t();else if("function"==typeof define&&define.amd)define([],t);else{var n=t();for(var l in n)("object"==typeof exports?exports:e)[l]=n[l]}}("undefined"!=typeof self?self:this,(function(){return function(){"use strict";var e={},t={inline:["$","$"],display:["$$","$$"]},n=function(e,n){void 0===n&&(n=t);for(var l=e.querySelectorAll(".katex-mathml + .katex-html"),r=0;r<l.length;r++){var i=l[r];i.remove?i.remove(null):i.parentNode.removeChild(i)}for(var o=e.querySelectorAll(".katex-mathml"),a=0;a<o.length;a++){var d=o[a],f=d.querySelector("annotation");f&&(d.replaceWith?d.replaceWith(f):d.parentNode.replaceChild(f,d),f.innerHTML=n.inline[0]+f.innerHTML+n.inline[1])}for(var c=e.querySelectorAll(".katex-display annotation"),s=0;s<c.length;s++){var p=c[s];p.innerHTML=n.display[0]+p.innerHTML.substr(n.inline[0].length,p.innerHTML.length-n.inline[0].length-n.inline[1].length)+n.display[1]}return e};return document.addEventListener("copy",(function(e){var t=window.getSelection();if(!t.isCollapsed){var l=t.getRangeAt(0).cloneContents();if(l.querySelector(".katex-mathml")){for(var r=[],i=0;i<l.childNodes.length;i++)r.push(l.childNodes[i].outerHTML);e.clipboardData.setData("text/html",r.join("")),e.clipboardData.setData("text/plain",n(l).textContent),e.preventDefault()}}})),e=e.default}()}));

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// Set these to how you want inline and display math to be delimited.
var defaultCopyDelimiters = {
inline: ['$', '$'],
// alternative: ['\(', '\)']
display: ['$$', '$$'] // alternative: ['\[', '\]']
}; // Replace .katex elements with their TeX source (<annotation> element).
// Modifies fragment in-place. Useful for writing your own 'copy' handler,
// as in copy-tex.js.
var katexReplaceWithTex = function katexReplaceWithTex(fragment, copyDelimiters) {
if (copyDelimiters === void 0) {
copyDelimiters = defaultCopyDelimiters;
}
// Remove .katex-html blocks that are preceded by .katex-mathml blocks
// (which will get replaced below).
var katexHtml = fragment.querySelectorAll('.katex-mathml + .katex-html');
for (var i = 0; i < katexHtml.length; i++) {
var element = katexHtml[i];
if (element.remove) {
element.remove(null);
} else {
element.parentNode.removeChild(element);
}
} // Replace .katex-mathml elements with their annotation (TeX source)
// descendant, with inline delimiters.
var katexMathml = fragment.querySelectorAll('.katex-mathml');
for (var _i = 0; _i < katexMathml.length; _i++) {
var _element = katexMathml[_i];
var texSource = _element.querySelector('annotation');
if (texSource) {
if (_element.replaceWith) {
_element.replaceWith(texSource);
} else {
_element.parentNode.replaceChild(texSource, _element);
}
texSource.innerHTML = copyDelimiters.inline[0] + texSource.innerHTML + copyDelimiters.inline[1];
}
} // Switch display math to display delimiters.
var displays = fragment.querySelectorAll('.katex-display annotation');
for (var _i2 = 0; _i2 < displays.length; _i2++) {
var _element2 = displays[_i2];
_element2.innerHTML = copyDelimiters.display[0] + _element2.innerHTML.substr(copyDelimiters.inline[0].length, _element2.innerHTML.length - copyDelimiters.inline[0].length - copyDelimiters.inline[1].length) + copyDelimiters.display[1];
}
return fragment;
};
document.addEventListener('copy', function (event) {
var selection = window.getSelection();
if (selection.isCollapsed) {
return; // default action OK if selection is empty
}
var fragment = selection.getRangeAt(0).cloneContents();
if (!fragment.querySelector('.katex-mathml')) {
return; // default action OK if no .katex-mathml elements
} // Preserve usual HTML copy/paste behavior.
var html = [];
for (var i = 0; i < fragment.childNodes.length; i++) {
html.push(fragment.childNodes[i].outerHTML);
}
event.clipboardData.setData('text/html', html.join('')); // Rewrite plain-text version.
event.clipboardData.setData('text/plain', katexReplaceWithTex(fragment).textContent); // Prevent normal copy handling.
event.preventDefault();
});

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(function webpackUniversalModuleDefinition(root, factory) {
if(typeof exports === 'object' && typeof module === 'object')
module.exports = factory(require("katex"));
else if(typeof define === 'function' && define.amd)
define(["katex"], factory);
else {
var a = typeof exports === 'object' ? factory(require("katex")) : factory(root["katex"]);
for(var i in a) (typeof exports === 'object' ? exports : root)[i] = a[i];
}
})((typeof self !== 'undefined' ? self : this), function(__WEBPACK_EXTERNAL_MODULE__771__) {
return /******/ (function() { // webpackBootstrap
/******/ "use strict";
/******/ var __webpack_modules__ = ({
/***/ 771:
/***/ (function(module) {
module.exports = __WEBPACK_EXTERNAL_MODULE__771__;
/***/ })
/******/ });
/************************************************************************/
/******/ // The module cache
/******/ var __webpack_module_cache__ = {};
/******/
/******/ // The require function
/******/ function __webpack_require__(moduleId) {
/******/ // Check if module is in cache
/******/ var cachedModule = __webpack_module_cache__[moduleId];
/******/ if (cachedModule !== undefined) {
/******/ return cachedModule.exports;
/******/ }
/******/ // Create a new module (and put it into the cache)
/******/ var module = __webpack_module_cache__[moduleId] = {
/******/ // no module.id needed
/******/ // no module.loaded needed
/******/ exports: {}
/******/ };
/******/
/******/ // Execute the module function
/******/ __webpack_modules__[moduleId](module, module.exports, __webpack_require__);
/******/
/******/ // Return the exports of the module
/******/ return module.exports;
/******/ }
/******/
/************************************************************************/
/******/ /* webpack/runtime/compat get default export */
/******/ !function() {
/******/ // getDefaultExport function for compatibility with non-harmony modules
/******/ __webpack_require__.n = function(module) {
/******/ var getter = module && module.__esModule ?
/******/ function() { return module['default']; } :
/******/ function() { return module; };
/******/ __webpack_require__.d(getter, { a: getter });
/******/ return getter;
/******/ };
/******/ }();
/******/
/******/ /* webpack/runtime/define property getters */
/******/ !function() {
/******/ // define getter functions for harmony exports
/******/ __webpack_require__.d = function(exports, definition) {
/******/ for(var key in definition) {
/******/ if(__webpack_require__.o(definition, key) && !__webpack_require__.o(exports, key)) {
/******/ Object.defineProperty(exports, key, { enumerable: true, get: definition[key] });
/******/ }
/******/ }
/******/ };
/******/ }();
/******/
/******/ /* webpack/runtime/hasOwnProperty shorthand */
/******/ !function() {
/******/ __webpack_require__.o = function(obj, prop) { return Object.prototype.hasOwnProperty.call(obj, prop); }
/******/ }();
/******/
/************************************************************************/
var __webpack_exports__ = {};
// This entry need to be wrapped in an IIFE because it need to be isolated against other modules in the chunk.
!function() {
/* harmony import */ var katex__WEBPACK_IMPORTED_MODULE_0__ = __webpack_require__(771);
/* harmony import */ var katex__WEBPACK_IMPORTED_MODULE_0___default = /*#__PURE__*/__webpack_require__.n(katex__WEBPACK_IMPORTED_MODULE_0__);
var scripts = document.body.getElementsByTagName("script");
scripts = Array.prototype.slice.call(scripts);
scripts.forEach(function (script) {
if (!script.type || !script.type.match(/math\/tex/i)) {
return -1;
}
var display = script.type.match(/mode\s*=\s*display(;|\s|\n|$)/) != null;
var katexElement = document.createElement(display ? "div" : "span");
katexElement.setAttribute("class", display ? "equation" : "inline-equation");
try {
katex__WEBPACK_IMPORTED_MODULE_0___default().render(script.text, katexElement, {
displayMode: display
});
} catch (err) {
//console.error(err); linter doesn't like this
katexElement.textContent = script.text;
}
script.parentNode.replaceChild(katexElement, script);
});
}();
__webpack_exports__ = __webpack_exports__["default"];
/******/ return __webpack_exports__;
/******/ })()
;
});

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!function(e,t){if("object"==typeof exports&&"object"==typeof module)module.exports=t(require("katex"));else if("function"==typeof define&&define.amd)define(["katex"],t);else{var r="object"==typeof exports?t(require("katex")):t(e.katex);for(var n in r)("object"==typeof exports?exports:e)[n]=r[n]}}("undefined"!=typeof self?self:this,(function(e){return function(){"use strict";var t={771:function(t){t.exports=e}},r={};function n(e){var o=r[e];if(void 0!==o)return o.exports;var i=r[e]={exports:{}};return t[e](i,i.exports,n),i.exports}n.n=function(e){var t=e&&e.__esModule?function(){return e.default}:function(){return e};return n.d(t,{a:t}),t},n.d=function(e,t){for(var r in t)n.o(t,r)&&!n.o(e,r)&&Object.defineProperty(e,r,{enumerable:!0,get:t[r]})},n.o=function(e,t){return Object.prototype.hasOwnProperty.call(e,t)};var o,i,a,u={};return o=n(771),i=n.n(o),a=document.body.getElementsByTagName("script"),(a=Array.prototype.slice.call(a)).forEach((function(e){if(!e.type||!e.type.match(/math\/tex/i))return-1;var t=null!=e.type.match(/mode\s*=\s*display(;|\s|\n|$)/),r=document.createElement(t?"div":"span");r.setAttribute("class",t?"equation":"inline-equation");try{i().render(e.text,r,{displayMode:t})}catch(t){r.textContent=e.text}e.parentNode.replaceChild(r,e)})),u=u.default}()}));

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import katex from '../katex.mjs';
var scripts = document.body.getElementsByTagName("script");
scripts = Array.prototype.slice.call(scripts);
scripts.forEach(function (script) {
if (!script.type || !script.type.match(/math\/tex/i)) {
return -1;
}
var display = script.type.match(/mode\s*=\s*display(;|\s|\n|$)/) != null;
var katexElement = document.createElement(display ? "div" : "span");
katexElement.setAttribute("class", display ? "equation" : "inline-equation");
try {
katex.render(script.text, katexElement, {
displayMode: display
});
} catch (err) {
//console.error(err); linter doesn't like this
katexElement.textContent = script.text;
}
script.parentNode.replaceChild(katexElement, script);
});

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(function webpackUniversalModuleDefinition(root, factory) {
if(typeof exports === 'object' && typeof module === 'object')
module.exports = factory(require("katex"));
else if(typeof define === 'function' && define.amd)
define(["katex"], factory);
else {
var a = typeof exports === 'object' ? factory(require("katex")) : factory(root["katex"]);
for(var i in a) (typeof exports === 'object' ? exports : root)[i] = a[i];
}
})((typeof self !== 'undefined' ? self : this), function(__WEBPACK_EXTERNAL_MODULE__771__) {
return /******/ (function() { // webpackBootstrap
/******/ "use strict";
/******/ var __webpack_modules__ = ({
/***/ 771:
/***/ (function(module) {
module.exports = __WEBPACK_EXTERNAL_MODULE__771__;
/***/ })
/******/ });
/************************************************************************/
/******/ // The module cache
/******/ var __webpack_module_cache__ = {};
/******/
/******/ // The require function
/******/ function __webpack_require__(moduleId) {
/******/ // Check if module is in cache
/******/ var cachedModule = __webpack_module_cache__[moduleId];
/******/ if (cachedModule !== undefined) {
/******/ return cachedModule.exports;
/******/ }
/******/ // Create a new module (and put it into the cache)
/******/ var module = __webpack_module_cache__[moduleId] = {
/******/ // no module.id needed
/******/ // no module.loaded needed
/******/ exports: {}
/******/ };
/******/
/******/ // Execute the module function
/******/ __webpack_modules__[moduleId](module, module.exports, __webpack_require__);
/******/
/******/ // Return the exports of the module
/******/ return module.exports;
/******/ }
/******/
/************************************************************************/
/******/ /* webpack/runtime/compat get default export */
/******/ !function() {
/******/ // getDefaultExport function for compatibility with non-harmony modules
/******/ __webpack_require__.n = function(module) {
/******/ var getter = module && module.__esModule ?
/******/ function() { return module['default']; } :
/******/ function() { return module; };
/******/ __webpack_require__.d(getter, { a: getter });
/******/ return getter;
/******/ };
/******/ }();
/******/
/******/ /* webpack/runtime/define property getters */
/******/ !function() {
/******/ // define getter functions for harmony exports
/******/ __webpack_require__.d = function(exports, definition) {
/******/ for(var key in definition) {
/******/ if(__webpack_require__.o(definition, key) && !__webpack_require__.o(exports, key)) {
/******/ Object.defineProperty(exports, key, { enumerable: true, get: definition[key] });
/******/ }
/******/ }
/******/ };
/******/ }();
/******/
/******/ /* webpack/runtime/hasOwnProperty shorthand */
/******/ !function() {
/******/ __webpack_require__.o = function(obj, prop) { return Object.prototype.hasOwnProperty.call(obj, prop); }
/******/ }();
/******/
/************************************************************************/
var __webpack_exports__ = {};
// This entry need to be wrapped in an IIFE because it need to be isolated against other modules in the chunk.
!function() {
/* harmony import */ var katex__WEBPACK_IMPORTED_MODULE_0__ = __webpack_require__(771);
/* harmony import */ var katex__WEBPACK_IMPORTED_MODULE_0___default = /*#__PURE__*/__webpack_require__.n(katex__WEBPACK_IMPORTED_MODULE_0__);
/**
* renderA11yString returns a readable string.
*
* In some cases the string will have the proper semantic math
* meaning,:
* renderA11yString("\\frac{1}{2}"")
* -> "start fraction, 1, divided by, 2, end fraction"
*
* However, other cases do not:
* renderA11yString("f(x) = x^2")
* -> "f, left parenthesis, x, right parenthesis, equals, x, squared"
*
* The commas in the string aim to increase ease of understanding
* when read by a screenreader.
*/
// NOTE: since we're importing types here these files won't actually be
// included in the build.
// $FlowIgnore: we import the types directly anyways
var stringMap = {
"(": "left parenthesis",
")": "right parenthesis",
"[": "open bracket",
"]": "close bracket",
"\\{": "left brace",
"\\}": "right brace",
"\\lvert": "open vertical bar",
"\\rvert": "close vertical bar",
"|": "vertical bar",
"\\uparrow": "up arrow",
"\\Uparrow": "up arrow",
"\\downarrow": "down arrow",
"\\Downarrow": "down arrow",
"\\updownarrow": "up down arrow",
"\\leftarrow": "left arrow",
"\\Leftarrow": "left arrow",
"\\rightarrow": "right arrow",
"\\Rightarrow": "right arrow",
"\\langle": "open angle",
"\\rangle": "close angle",
"\\lfloor": "open floor",
"\\rfloor": "close floor",
"\\int": "integral",
"\\intop": "integral",
"\\lim": "limit",
"\\ln": "natural log",
"\\log": "log",
"\\sin": "sine",
"\\cos": "cosine",
"\\tan": "tangent",
"\\cot": "cotangent",
"\\sum": "sum",
"/": "slash",
",": "comma",
".": "point",
"-": "negative",
"+": "plus",
"~": "tilde",
":": "colon",
"?": "question mark",
"'": "apostrophe",
"\\%": "percent",
" ": "space",
"\\ ": "space",
"\\$": "dollar sign",
"\\angle": "angle",
"\\degree": "degree",
"\\circ": "circle",
"\\vec": "vector",
"\\triangle": "triangle",
"\\pi": "pi",
"\\prime": "prime",
"\\infty": "infinity",
"\\alpha": "alpha",
"\\beta": "beta",
"\\gamma": "gamma",
"\\omega": "omega",
"\\theta": "theta",
"\\sigma": "sigma",
"\\lambda": "lambda",
"\\tau": "tau",
"\\Delta": "delta",
"\\delta": "delta",
"\\mu": "mu",
"\\rho": "rho",
"\\nabla": "del",
"\\ell": "ell",
"\\ldots": "dots",
// TODO: add entries for all accents
"\\hat": "hat",
"\\acute": "acute"
};
var powerMap = {
"prime": "prime",
"degree": "degrees",
"circle": "degrees",
"2": "squared",
"3": "cubed"
};
var openMap = {
"|": "open vertical bar",
".": ""
};
var closeMap = {
"|": "close vertical bar",
".": ""
};
var binMap = {
"+": "plus",
"-": "minus",
"\\pm": "plus minus",
"\\cdot": "dot",
"*": "times",
"/": "divided by",
"\\times": "times",
"\\div": "divided by",
"\\circ": "circle",
"\\bullet": "bullet"
};
var relMap = {
"=": "equals",
"\\approx": "approximately equals",
"≠": "does not equal",
"\\geq": "is greater than or equal to",
"\\ge": "is greater than or equal to",
"\\leq": "is less than or equal to",
"\\le": "is less than or equal to",
">": "is greater than",
"<": "is less than",
"\\leftarrow": "left arrow",
"\\Leftarrow": "left arrow",
"\\rightarrow": "right arrow",
"\\Rightarrow": "right arrow",
":": "colon"
};
var accentUnderMap = {
"\\underleftarrow": "left arrow",
"\\underrightarrow": "right arrow",
"\\underleftrightarrow": "left-right arrow",
"\\undergroup": "group",
"\\underlinesegment": "line segment",
"\\utilde": "tilde"
};
var buildString = function buildString(str, type, a11yStrings) {
if (!str) {
return;
}
var ret;
if (type === "open") {
ret = str in openMap ? openMap[str] : stringMap[str] || str;
} else if (type === "close") {
ret = str in closeMap ? closeMap[str] : stringMap[str] || str;
} else if (type === "bin") {
ret = binMap[str] || str;
} else if (type === "rel") {
ret = relMap[str] || str;
} else {
ret = stringMap[str] || str;
} // If the text to add is a number and there is already a string
// in the list and the last string is a number then we should
// combine them into a single number
if (/^\d+$/.test(ret) && a11yStrings.length > 0 && // TODO(kevinb): check that the last item in a11yStrings is a string
// I think we might be able to drop the nested arrays, which would make
// this easier to type
// $FlowFixMe
/^\d+$/.test(a11yStrings[a11yStrings.length - 1])) {
a11yStrings[a11yStrings.length - 1] += ret;
} else if (ret) {
a11yStrings.push(ret);
}
};
var buildRegion = function buildRegion(a11yStrings, callback) {
var regionStrings = [];
a11yStrings.push(regionStrings);
callback(regionStrings);
};
var handleObject = function handleObject(tree, a11yStrings, atomType) {
// Everything else is assumed to be an object...
switch (tree.type) {
case "accent":
{
buildRegion(a11yStrings, function (a11yStrings) {
buildA11yStrings(tree.base, a11yStrings, atomType);
a11yStrings.push("with");
buildString(tree.label, "normal", a11yStrings);
a11yStrings.push("on top");
});
break;
}
case "accentUnder":
{
buildRegion(a11yStrings, function (a11yStrings) {
buildA11yStrings(tree.base, a11yStrings, atomType);
a11yStrings.push("with");
buildString(accentUnderMap[tree.label], "normal", a11yStrings);
a11yStrings.push("underneath");
});
break;
}
case "accent-token":
{
// Used internally by accent symbols.
break;
}
case "atom":
{
var text = tree.text;
switch (tree.family) {
case "bin":
{
buildString(text, "bin", a11yStrings);
break;
}
case "close":
{
buildString(text, "close", a11yStrings);
break;
}
// TODO(kevinb): figure out what should be done for inner
case "inner":
{
buildString(tree.text, "inner", a11yStrings);
break;
}
case "open":
{
buildString(text, "open", a11yStrings);
break;
}
case "punct":
{
buildString(text, "punct", a11yStrings);
break;
}
case "rel":
{
buildString(text, "rel", a11yStrings);
break;
}
default:
{
tree.family;
throw new Error("\"" + tree.family + "\" is not a valid atom type");
}
}
break;
}
case "color":
{
var color = tree.color.replace(/katex-/, "");
buildRegion(a11yStrings, function (regionStrings) {
regionStrings.push("start color " + color);
buildA11yStrings(tree.body, regionStrings, atomType);
regionStrings.push("end color " + color);
});
break;
}
case "color-token":
{
// Used by \color, \colorbox, and \fcolorbox but not directly rendered.
// It's a leaf node and has no children so just break.
break;
}
case "delimsizing":
{
if (tree.delim && tree.delim !== ".") {
buildString(tree.delim, "normal", a11yStrings);
}
break;
}
case "genfrac":
{
buildRegion(a11yStrings, function (regionStrings) {
// genfrac can have unbalanced delimiters
var leftDelim = tree.leftDelim,
rightDelim = tree.rightDelim; // NOTE: Not sure if this is a safe assumption
// hasBarLine true -> fraction, false -> binomial
if (tree.hasBarLine) {
regionStrings.push("start fraction");
leftDelim && buildString(leftDelim, "open", regionStrings);
buildA11yStrings(tree.numer, regionStrings, atomType);
regionStrings.push("divided by");
buildA11yStrings(tree.denom, regionStrings, atomType);
rightDelim && buildString(rightDelim, "close", regionStrings);
regionStrings.push("end fraction");
} else {
regionStrings.push("start binomial");
leftDelim && buildString(leftDelim, "open", regionStrings);
buildA11yStrings(tree.numer, regionStrings, atomType);
regionStrings.push("over");
buildA11yStrings(tree.denom, regionStrings, atomType);
rightDelim && buildString(rightDelim, "close", regionStrings);
regionStrings.push("end binomial");
}
});
break;
}
case "hbox":
{
buildA11yStrings(tree.body, a11yStrings, atomType);
break;
}
case "kern":
{
// No op: we don't attempt to present kerning information
// to the screen reader.
break;
}
case "leftright":
{
buildRegion(a11yStrings, function (regionStrings) {
buildString(tree.left, "open", regionStrings);
buildA11yStrings(tree.body, regionStrings, atomType);
buildString(tree.right, "close", regionStrings);
});
break;
}
case "leftright-right":
{
// TODO: double check that this is a no-op
break;
}
case "lap":
{
buildA11yStrings(tree.body, a11yStrings, atomType);
break;
}
case "mathord":
{
buildString(tree.text, "normal", a11yStrings);
break;
}
case "op":
{
var body = tree.body,
name = tree.name;
if (body) {
buildA11yStrings(body, a11yStrings, atomType);
} else if (name) {
buildString(name, "normal", a11yStrings);
}
break;
}
case "op-token":
{
// Used internally by operator symbols.
buildString(tree.text, atomType, a11yStrings);
break;
}
case "ordgroup":
{
buildA11yStrings(tree.body, a11yStrings, atomType);
break;
}
case "overline":
{
buildRegion(a11yStrings, function (a11yStrings) {
a11yStrings.push("start overline");
buildA11yStrings(tree.body, a11yStrings, atomType);
a11yStrings.push("end overline");
});
break;
}
case "phantom":
{
a11yStrings.push("empty space");
break;
}
case "raisebox":
{
buildA11yStrings(tree.body, a11yStrings, atomType);
break;
}
case "rule":
{
a11yStrings.push("rectangle");
break;
}
case "sizing":
{
buildA11yStrings(tree.body, a11yStrings, atomType);
break;
}
case "spacing":
{
a11yStrings.push("space");
break;
}
case "styling":
{
// We ignore the styling and just pass through the contents
buildA11yStrings(tree.body, a11yStrings, atomType);
break;
}
case "sqrt":
{
buildRegion(a11yStrings, function (regionStrings) {
var body = tree.body,
index = tree.index;
if (index) {
var indexString = flatten(buildA11yStrings(index, [], atomType)).join(",");
if (indexString === "3") {
regionStrings.push("cube root of");
buildA11yStrings(body, regionStrings, atomType);
regionStrings.push("end cube root");
return;
}
regionStrings.push("root");
regionStrings.push("start index");
buildA11yStrings(index, regionStrings, atomType);
regionStrings.push("end index");
return;
}
regionStrings.push("square root of");
buildA11yStrings(body, regionStrings, atomType);
regionStrings.push("end square root");
});
break;
}
case "supsub":
{
var base = tree.base,
sub = tree.sub,
sup = tree.sup;
var isLog = false;
if (base) {
buildA11yStrings(base, a11yStrings, atomType);
isLog = base.type === "op" && base.name === "\\log";
}
if (sub) {
var regionName = isLog ? "base" : "subscript";
buildRegion(a11yStrings, function (regionStrings) {
regionStrings.push("start " + regionName);
buildA11yStrings(sub, regionStrings, atomType);
regionStrings.push("end " + regionName);
});
}
if (sup) {
buildRegion(a11yStrings, function (regionStrings) {
var supString = flatten(buildA11yStrings(sup, [], atomType)).join(",");
if (supString in powerMap) {
regionStrings.push(powerMap[supString]);
return;
}
regionStrings.push("start superscript");
buildA11yStrings(sup, regionStrings, atomType);
regionStrings.push("end superscript");
});
}
break;
}
case "text":
{
// TODO: handle other fonts
if (tree.font === "\\textbf") {
buildRegion(a11yStrings, function (regionStrings) {
regionStrings.push("start bold text");
buildA11yStrings(tree.body, regionStrings, atomType);
regionStrings.push("end bold text");
});
break;
}
buildRegion(a11yStrings, function (regionStrings) {
regionStrings.push("start text");
buildA11yStrings(tree.body, regionStrings, atomType);
regionStrings.push("end text");
});
break;
}
case "textord":
{
buildString(tree.text, atomType, a11yStrings);
break;
}
case "smash":
{
buildA11yStrings(tree.body, a11yStrings, atomType);
break;
}
case "enclose":
{
// TODO: create a map for these.
// TODO: differentiate between a body with a single atom, e.g.
// "cancel a" instead of "start cancel, a, end cancel"
if (/cancel/.test(tree.label)) {
buildRegion(a11yStrings, function (regionStrings) {
regionStrings.push("start cancel");
buildA11yStrings(tree.body, regionStrings, atomType);
regionStrings.push("end cancel");
});
break;
} else if (/box/.test(tree.label)) {
buildRegion(a11yStrings, function (regionStrings) {
regionStrings.push("start box");
buildA11yStrings(tree.body, regionStrings, atomType);
regionStrings.push("end box");
});
break;
} else if (/sout/.test(tree.label)) {
buildRegion(a11yStrings, function (regionStrings) {
regionStrings.push("start strikeout");
buildA11yStrings(tree.body, regionStrings, atomType);
regionStrings.push("end strikeout");
});
break;
} else if (/phase/.test(tree.label)) {
buildRegion(a11yStrings, function (regionStrings) {
regionStrings.push("start phase angle");
buildA11yStrings(tree.body, regionStrings, atomType);
regionStrings.push("end phase angle");
});
break;
}
throw new Error("KaTeX-a11y: enclose node with " + tree.label + " not supported yet");
}
case "vcenter":
{
buildA11yStrings(tree.body, a11yStrings, atomType);
break;
}
case "vphantom":
{
throw new Error("KaTeX-a11y: vphantom not implemented yet");
}
case "hphantom":
{
throw new Error("KaTeX-a11y: hphantom not implemented yet");
}
case "operatorname":
{
buildA11yStrings(tree.body, a11yStrings, atomType);
break;
}
case "array":
{
throw new Error("KaTeX-a11y: array not implemented yet");
}
case "raw":
{
throw new Error("KaTeX-a11y: raw not implemented yet");
}
case "size":
{
// Although there are nodes of type "size" in the parse tree, they have
// no semantic meaning and should be ignored.
break;
}
case "url":
{
throw new Error("KaTeX-a11y: url not implemented yet");
}
case "tag":
{
throw new Error("KaTeX-a11y: tag not implemented yet");
}
case "verb":
{
buildString("start verbatim", "normal", a11yStrings);
buildString(tree.body, "normal", a11yStrings);
buildString("end verbatim", "normal", a11yStrings);
break;
}
case "environment":
{
throw new Error("KaTeX-a11y: environment not implemented yet");
}
case "horizBrace":
{
buildString("start " + tree.label.slice(1), "normal", a11yStrings);
buildA11yStrings(tree.base, a11yStrings, atomType);
buildString("end " + tree.label.slice(1), "normal", a11yStrings);
break;
}
case "infix":
{
// All infix nodes are replace with other nodes.
break;
}
case "includegraphics":
{
throw new Error("KaTeX-a11y: includegraphics not implemented yet");
}
case "font":
{
// TODO: callout the start/end of specific fonts
// TODO: map \BBb{N} to "the naturals" or something like that
buildA11yStrings(tree.body, a11yStrings, atomType);
break;
}
case "href":
{
throw new Error("KaTeX-a11y: href not implemented yet");
}
case "cr":
{
// This is used by environments.
throw new Error("KaTeX-a11y: cr not implemented yet");
}
case "underline":
{
buildRegion(a11yStrings, function (a11yStrings) {
a11yStrings.push("start underline");
buildA11yStrings(tree.body, a11yStrings, atomType);
a11yStrings.push("end underline");
});
break;
}
case "xArrow":
{
throw new Error("KaTeX-a11y: xArrow not implemented yet");
}
case "cdlabel":
{
throw new Error("KaTeX-a11y: cdlabel not implemented yet");
}
case "cdlabelparent":
{
throw new Error("KaTeX-a11y: cdlabelparent not implemented yet");
}
case "mclass":
{
// \neq and \ne are macros so we let "htmlmathml" render the mathmal
// side of things and extract the text from that.
var _atomType = tree.mclass.slice(1); // $FlowFixMe: drop the leading "m" from the values in mclass
buildA11yStrings(tree.body, a11yStrings, _atomType);
break;
}
case "mathchoice":
{
// TODO: track which which style we're using, e.g. dispaly, text, etc.
// default to text style if even that may not be the correct style
buildA11yStrings(tree.text, a11yStrings, atomType);
break;
}
case "htmlmathml":
{
buildA11yStrings(tree.mathml, a11yStrings, atomType);
break;
}
case "middle":
{
buildString(tree.delim, atomType, a11yStrings);
break;
}
case "internal":
{
// internal nodes are never included in the parse tree
break;
}
case "html":
{
buildA11yStrings(tree.body, a11yStrings, atomType);
break;
}
default:
tree.type;
throw new Error("KaTeX a11y un-recognized type: " + tree.type);
}
};
var buildA11yStrings = function buildA11yStrings(tree, a11yStrings, atomType) {
if (a11yStrings === void 0) {
a11yStrings = [];
}
if (tree instanceof Array) {
for (var i = 0; i < tree.length; i++) {
buildA11yStrings(tree[i], a11yStrings, atomType);
}
} else {
handleObject(tree, a11yStrings, atomType);
}
return a11yStrings;
};
var flatten = function flatten(array) {
var result = [];
array.forEach(function (item) {
if (item instanceof Array) {
result = result.concat(flatten(item));
} else {
result.push(item);
}
});
return result;
};
var renderA11yString = function renderA11yString(text, settings) {
var tree = katex__WEBPACK_IMPORTED_MODULE_0___default().__parse(text, settings);
var a11yStrings = buildA11yStrings(tree, [], "normal");
return flatten(a11yStrings).join(", ");
};
/* harmony default export */ __webpack_exports__["default"] = (renderA11yString);
}();
__webpack_exports__ = __webpack_exports__["default"];
/******/ return __webpack_exports__;
/******/ })()
;
});

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import katex from '../katex.mjs';
/**
* renderA11yString returns a readable string.
*
* In some cases the string will have the proper semantic math
* meaning,:
* renderA11yString("\\frac{1}{2}"")
* -> "start fraction, 1, divided by, 2, end fraction"
*
* However, other cases do not:
* renderA11yString("f(x) = x^2")
* -> "f, left parenthesis, x, right parenthesis, equals, x, squared"
*
* The commas in the string aim to increase ease of understanding
* when read by a screenreader.
*/
var stringMap = {
"(": "left parenthesis",
")": "right parenthesis",
"[": "open bracket",
"]": "close bracket",
"\\{": "left brace",
"\\}": "right brace",
"\\lvert": "open vertical bar",
"\\rvert": "close vertical bar",
"|": "vertical bar",
"\\uparrow": "up arrow",
"\\Uparrow": "up arrow",
"\\downarrow": "down arrow",
"\\Downarrow": "down arrow",
"\\updownarrow": "up down arrow",
"\\leftarrow": "left arrow",
"\\Leftarrow": "left arrow",
"\\rightarrow": "right arrow",
"\\Rightarrow": "right arrow",
"\\langle": "open angle",
"\\rangle": "close angle",
"\\lfloor": "open floor",
"\\rfloor": "close floor",
"\\int": "integral",
"\\intop": "integral",
"\\lim": "limit",
"\\ln": "natural log",
"\\log": "log",
"\\sin": "sine",
"\\cos": "cosine",
"\\tan": "tangent",
"\\cot": "cotangent",
"\\sum": "sum",
"/": "slash",
",": "comma",
".": "point",
"-": "negative",
"+": "plus",
"~": "tilde",
":": "colon",
"?": "question mark",
"'": "apostrophe",
"\\%": "percent",
" ": "space",
"\\ ": "space",
"\\$": "dollar sign",
"\\angle": "angle",
"\\degree": "degree",
"\\circ": "circle",
"\\vec": "vector",
"\\triangle": "triangle",
"\\pi": "pi",
"\\prime": "prime",
"\\infty": "infinity",
"\\alpha": "alpha",
"\\beta": "beta",
"\\gamma": "gamma",
"\\omega": "omega",
"\\theta": "theta",
"\\sigma": "sigma",
"\\lambda": "lambda",
"\\tau": "tau",
"\\Delta": "delta",
"\\delta": "delta",
"\\mu": "mu",
"\\rho": "rho",
"\\nabla": "del",
"\\ell": "ell",
"\\ldots": "dots",
// TODO: add entries for all accents
"\\hat": "hat",
"\\acute": "acute"
};
var powerMap = {
"prime": "prime",
"degree": "degrees",
"circle": "degrees",
"2": "squared",
"3": "cubed"
};
var openMap = {
"|": "open vertical bar",
".": ""
};
var closeMap = {
"|": "close vertical bar",
".": ""
};
var binMap = {
"+": "plus",
"-": "minus",
"\\pm": "plus minus",
"\\cdot": "dot",
"*": "times",
"/": "divided by",
"\\times": "times",
"\\div": "divided by",
"\\circ": "circle",
"\\bullet": "bullet"
};
var relMap = {
"=": "equals",
"\\approx": "approximately equals",
"≠": "does not equal",
"\\geq": "is greater than or equal to",
"\\ge": "is greater than or equal to",
"\\leq": "is less than or equal to",
"\\le": "is less than or equal to",
">": "is greater than",
"<": "is less than",
"\\leftarrow": "left arrow",
"\\Leftarrow": "left arrow",
"\\rightarrow": "right arrow",
"\\Rightarrow": "right arrow",
":": "colon"
};
var accentUnderMap = {
"\\underleftarrow": "left arrow",
"\\underrightarrow": "right arrow",
"\\underleftrightarrow": "left-right arrow",
"\\undergroup": "group",
"\\underlinesegment": "line segment",
"\\utilde": "tilde"
};
var buildString = (str, type, a11yStrings) => {
if (!str) {
return;
}
var ret;
if (type === "open") {
ret = str in openMap ? openMap[str] : stringMap[str] || str;
} else if (type === "close") {
ret = str in closeMap ? closeMap[str] : stringMap[str] || str;
} else if (type === "bin") {
ret = binMap[str] || str;
} else if (type === "rel") {
ret = relMap[str] || str;
} else {
ret = stringMap[str] || str;
} // If the text to add is a number and there is already a string
// in the list and the last string is a number then we should
// combine them into a single number
if (/^\d+$/.test(ret) && a11yStrings.length > 0 && // TODO(kevinb): check that the last item in a11yStrings is a string
// I think we might be able to drop the nested arrays, which would make
// this easier to type
// $FlowFixMe
/^\d+$/.test(a11yStrings[a11yStrings.length - 1])) {
a11yStrings[a11yStrings.length - 1] += ret;
} else if (ret) {
a11yStrings.push(ret);
}
};
var buildRegion = (a11yStrings, callback) => {
var regionStrings = [];
a11yStrings.push(regionStrings);
callback(regionStrings);
};
var handleObject = (tree, a11yStrings, atomType) => {
// Everything else is assumed to be an object...
switch (tree.type) {
case "accent":
{
buildRegion(a11yStrings, a11yStrings => {
buildA11yStrings(tree.base, a11yStrings, atomType);
a11yStrings.push("with");
buildString(tree.label, "normal", a11yStrings);
a11yStrings.push("on top");
});
break;
}
case "accentUnder":
{
buildRegion(a11yStrings, a11yStrings => {
buildA11yStrings(tree.base, a11yStrings, atomType);
a11yStrings.push("with");
buildString(accentUnderMap[tree.label], "normal", a11yStrings);
a11yStrings.push("underneath");
});
break;
}
case "accent-token":
{
// Used internally by accent symbols.
break;
}
case "atom":
{
var {
text
} = tree;
switch (tree.family) {
case "bin":
{
buildString(text, "bin", a11yStrings);
break;
}
case "close":
{
buildString(text, "close", a11yStrings);
break;
}
// TODO(kevinb): figure out what should be done for inner
case "inner":
{
buildString(tree.text, "inner", a11yStrings);
break;
}
case "open":
{
buildString(text, "open", a11yStrings);
break;
}
case "punct":
{
buildString(text, "punct", a11yStrings);
break;
}
case "rel":
{
buildString(text, "rel", a11yStrings);
break;
}
default:
{
tree.family;
throw new Error("\"" + tree.family + "\" is not a valid atom type");
}
}
break;
}
case "color":
{
var color = tree.color.replace(/katex-/, "");
buildRegion(a11yStrings, regionStrings => {
regionStrings.push("start color " + color);
buildA11yStrings(tree.body, regionStrings, atomType);
regionStrings.push("end color " + color);
});
break;
}
case "color-token":
{
// Used by \color, \colorbox, and \fcolorbox but not directly rendered.
// It's a leaf node and has no children so just break.
break;
}
case "delimsizing":
{
if (tree.delim && tree.delim !== ".") {
buildString(tree.delim, "normal", a11yStrings);
}
break;
}
case "genfrac":
{
buildRegion(a11yStrings, regionStrings => {
// genfrac can have unbalanced delimiters
var {
leftDelim,
rightDelim
} = tree; // NOTE: Not sure if this is a safe assumption
// hasBarLine true -> fraction, false -> binomial
if (tree.hasBarLine) {
regionStrings.push("start fraction");
leftDelim && buildString(leftDelim, "open", regionStrings);
buildA11yStrings(tree.numer, regionStrings, atomType);
regionStrings.push("divided by");
buildA11yStrings(tree.denom, regionStrings, atomType);
rightDelim && buildString(rightDelim, "close", regionStrings);
regionStrings.push("end fraction");
} else {
regionStrings.push("start binomial");
leftDelim && buildString(leftDelim, "open", regionStrings);
buildA11yStrings(tree.numer, regionStrings, atomType);
regionStrings.push("over");
buildA11yStrings(tree.denom, regionStrings, atomType);
rightDelim && buildString(rightDelim, "close", regionStrings);
regionStrings.push("end binomial");
}
});
break;
}
case "hbox":
{
buildA11yStrings(tree.body, a11yStrings, atomType);
break;
}
case "kern":
{
// No op: we don't attempt to present kerning information
// to the screen reader.
break;
}
case "leftright":
{
buildRegion(a11yStrings, regionStrings => {
buildString(tree.left, "open", regionStrings);
buildA11yStrings(tree.body, regionStrings, atomType);
buildString(tree.right, "close", regionStrings);
});
break;
}
case "leftright-right":
{
// TODO: double check that this is a no-op
break;
}
case "lap":
{
buildA11yStrings(tree.body, a11yStrings, atomType);
break;
}
case "mathord":
{
buildString(tree.text, "normal", a11yStrings);
break;
}
case "op":
{
var {
body,
name
} = tree;
if (body) {
buildA11yStrings(body, a11yStrings, atomType);
} else if (name) {
buildString(name, "normal", a11yStrings);
}
break;
}
case "op-token":
{
// Used internally by operator symbols.
buildString(tree.text, atomType, a11yStrings);
break;
}
case "ordgroup":
{
buildA11yStrings(tree.body, a11yStrings, atomType);
break;
}
case "overline":
{
buildRegion(a11yStrings, function (a11yStrings) {
a11yStrings.push("start overline");
buildA11yStrings(tree.body, a11yStrings, atomType);
a11yStrings.push("end overline");
});
break;
}
case "phantom":
{
a11yStrings.push("empty space");
break;
}
case "raisebox":
{
buildA11yStrings(tree.body, a11yStrings, atomType);
break;
}
case "rule":
{
a11yStrings.push("rectangle");
break;
}
case "sizing":
{
buildA11yStrings(tree.body, a11yStrings, atomType);
break;
}
case "spacing":
{
a11yStrings.push("space");
break;
}
case "styling":
{
// We ignore the styling and just pass through the contents
buildA11yStrings(tree.body, a11yStrings, atomType);
break;
}
case "sqrt":
{
buildRegion(a11yStrings, regionStrings => {
var {
body,
index
} = tree;
if (index) {
var indexString = flatten(buildA11yStrings(index, [], atomType)).join(",");
if (indexString === "3") {
regionStrings.push("cube root of");
buildA11yStrings(body, regionStrings, atomType);
regionStrings.push("end cube root");
return;
}
regionStrings.push("root");
regionStrings.push("start index");
buildA11yStrings(index, regionStrings, atomType);
regionStrings.push("end index");
return;
}
regionStrings.push("square root of");
buildA11yStrings(body, regionStrings, atomType);
regionStrings.push("end square root");
});
break;
}
case "supsub":
{
var {
base,
sub,
sup
} = tree;
var isLog = false;
if (base) {
buildA11yStrings(base, a11yStrings, atomType);
isLog = base.type === "op" && base.name === "\\log";
}
if (sub) {
var regionName = isLog ? "base" : "subscript";
buildRegion(a11yStrings, function (regionStrings) {
regionStrings.push("start " + regionName);
buildA11yStrings(sub, regionStrings, atomType);
regionStrings.push("end " + regionName);
});
}
if (sup) {
buildRegion(a11yStrings, function (regionStrings) {
var supString = flatten(buildA11yStrings(sup, [], atomType)).join(",");
if (supString in powerMap) {
regionStrings.push(powerMap[supString]);
return;
}
regionStrings.push("start superscript");
buildA11yStrings(sup, regionStrings, atomType);
regionStrings.push("end superscript");
});
}
break;
}
case "text":
{
// TODO: handle other fonts
if (tree.font === "\\textbf") {
buildRegion(a11yStrings, function (regionStrings) {
regionStrings.push("start bold text");
buildA11yStrings(tree.body, regionStrings, atomType);
regionStrings.push("end bold text");
});
break;
}
buildRegion(a11yStrings, function (regionStrings) {
regionStrings.push("start text");
buildA11yStrings(tree.body, regionStrings, atomType);
regionStrings.push("end text");
});
break;
}
case "textord":
{
buildString(tree.text, atomType, a11yStrings);
break;
}
case "smash":
{
buildA11yStrings(tree.body, a11yStrings, atomType);
break;
}
case "enclose":
{
// TODO: create a map for these.
// TODO: differentiate between a body with a single atom, e.g.
// "cancel a" instead of "start cancel, a, end cancel"
if (/cancel/.test(tree.label)) {
buildRegion(a11yStrings, function (regionStrings) {
regionStrings.push("start cancel");
buildA11yStrings(tree.body, regionStrings, atomType);
regionStrings.push("end cancel");
});
break;
} else if (/box/.test(tree.label)) {
buildRegion(a11yStrings, function (regionStrings) {
regionStrings.push("start box");
buildA11yStrings(tree.body, regionStrings, atomType);
regionStrings.push("end box");
});
break;
} else if (/sout/.test(tree.label)) {
buildRegion(a11yStrings, function (regionStrings) {
regionStrings.push("start strikeout");
buildA11yStrings(tree.body, regionStrings, atomType);
regionStrings.push("end strikeout");
});
break;
} else if (/phase/.test(tree.label)) {
buildRegion(a11yStrings, function (regionStrings) {
regionStrings.push("start phase angle");
buildA11yStrings(tree.body, regionStrings, atomType);
regionStrings.push("end phase angle");
});
break;
}
throw new Error("KaTeX-a11y: enclose node with " + tree.label + " not supported yet");
}
case "vcenter":
{
buildA11yStrings(tree.body, a11yStrings, atomType);
break;
}
case "vphantom":
{
throw new Error("KaTeX-a11y: vphantom not implemented yet");
}
case "hphantom":
{
throw new Error("KaTeX-a11y: hphantom not implemented yet");
}
case "operatorname":
{
buildA11yStrings(tree.body, a11yStrings, atomType);
break;
}
case "array":
{
throw new Error("KaTeX-a11y: array not implemented yet");
}
case "raw":
{
throw new Error("KaTeX-a11y: raw not implemented yet");
}
case "size":
{
// Although there are nodes of type "size" in the parse tree, they have
// no semantic meaning and should be ignored.
break;
}
case "url":
{
throw new Error("KaTeX-a11y: url not implemented yet");
}
case "tag":
{
throw new Error("KaTeX-a11y: tag not implemented yet");
}
case "verb":
{
buildString("start verbatim", "normal", a11yStrings);
buildString(tree.body, "normal", a11yStrings);
buildString("end verbatim", "normal", a11yStrings);
break;
}
case "environment":
{
throw new Error("KaTeX-a11y: environment not implemented yet");
}
case "horizBrace":
{
buildString("start " + tree.label.slice(1), "normal", a11yStrings);
buildA11yStrings(tree.base, a11yStrings, atomType);
buildString("end " + tree.label.slice(1), "normal", a11yStrings);
break;
}
case "infix":
{
// All infix nodes are replace with other nodes.
break;
}
case "includegraphics":
{
throw new Error("KaTeX-a11y: includegraphics not implemented yet");
}
case "font":
{
// TODO: callout the start/end of specific fonts
// TODO: map \BBb{N} to "the naturals" or something like that
buildA11yStrings(tree.body, a11yStrings, atomType);
break;
}
case "href":
{
throw new Error("KaTeX-a11y: href not implemented yet");
}
case "cr":
{
// This is used by environments.
throw new Error("KaTeX-a11y: cr not implemented yet");
}
case "underline":
{
buildRegion(a11yStrings, function (a11yStrings) {
a11yStrings.push("start underline");
buildA11yStrings(tree.body, a11yStrings, atomType);
a11yStrings.push("end underline");
});
break;
}
case "xArrow":
{
throw new Error("KaTeX-a11y: xArrow not implemented yet");
}
case "cdlabel":
{
throw new Error("KaTeX-a11y: cdlabel not implemented yet");
}
case "cdlabelparent":
{
throw new Error("KaTeX-a11y: cdlabelparent not implemented yet");
}
case "mclass":
{
// \neq and \ne are macros so we let "htmlmathml" render the mathmal
// side of things and extract the text from that.
var _atomType = tree.mclass.slice(1); // $FlowFixMe: drop the leading "m" from the values in mclass
buildA11yStrings(tree.body, a11yStrings, _atomType);
break;
}
case "mathchoice":
{
// TODO: track which which style we're using, e.g. dispaly, text, etc.
// default to text style if even that may not be the correct style
buildA11yStrings(tree.text, a11yStrings, atomType);
break;
}
case "htmlmathml":
{
buildA11yStrings(tree.mathml, a11yStrings, atomType);
break;
}
case "middle":
{
buildString(tree.delim, atomType, a11yStrings);
break;
}
case "internal":
{
// internal nodes are never included in the parse tree
break;
}
case "html":
{
buildA11yStrings(tree.body, a11yStrings, atomType);
break;
}
default:
tree.type;
throw new Error("KaTeX a11y un-recognized type: " + tree.type);
}
};
var buildA11yStrings = function buildA11yStrings(tree, a11yStrings, atomType) {
if (a11yStrings === void 0) {
a11yStrings = [];
}
if (tree instanceof Array) {
for (var i = 0; i < tree.length; i++) {
buildA11yStrings(tree[i], a11yStrings, atomType);
}
} else {
handleObject(tree, a11yStrings, atomType);
}
return a11yStrings;
};
var flatten = function flatten(array) {
var result = [];
array.forEach(function (item) {
if (item instanceof Array) {
result = result.concat(flatten(item));
} else {
result.push(item);
}
});
return result;
};
var renderA11yString = function renderA11yString(text, settings) {
var tree = katex.__parse(text, settings);
var a11yStrings = buildA11yStrings(tree, [], "normal");
return flatten(a11yStrings).join(", ");
};
export { renderA11yString as default };

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