peano:0.1.0

packages/preview/peano/0.1.0/LICENSE.txt

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+MIT License
+
+Copyright (c) 2025 F.X.P.
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.

packages/preview/peano/0.1.0/README.md

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+<!-- This is a program-generated file. Do not edit it directly. -->
+
+# Typst package: `peano`
+
+`peano` is a math utility package that provides you with representations of specialized number types, mathematic special functions, number theory related operations and so on. The name of the package comes from [Peano axioms](https://en.wikipedia.org/wiki/Peano_axioms), which builds up the framework of [natural numbers](https://en.wikipedia.org/wiki/Natural_number) &#x2115;, one of the the most elementary concepts in mathematics, aiming to convey this package's orientation as a simple utility package.
+
+## Number types
+
+`peano` currently supports two number types and their arithmetics:
+
+- `rational`: representation of [rational numbers](https://en.wikipedia.org/wiki/Rational_number) &#x211a; in the form of fractions
+- `complex`: representation of[ complex numbers](https://en.wikipedia.org/wiki/Complex_number) &#x2102;
+
+It is a pity that Typst doesn't currently support custom types and overloading operators, so actually these numbers are represented by Typst's `dictionary` type, and you have to invoke specialized methods in the corresponding sub-module to perform arithmetic operations over these numbers.
+
+To use these number types you have to first import the corresponding sub-module:
+
+```typ
+#import "@preview/peano:0.1.0"
+#import peano.number: rational as q, complex as c
+```
+
+Each sub-module contains a method called `from`, by which you can directly create a number instance from a string or a built-in Typst number type. Arithmetic methods in these modules will automatically convert all parameters to the expected number type by this `from` method, so you can simply input strings and built-in number types as parameters.
+
+### Rational numbers
+
+```typ
+#import "@preview/peano:0.1.0"
+#import peano.number: rational as q
+
+#q.from("1/2") // from string
+#q.from(2, 3) // from numerator and denominator
+#q.add("1/2", "1/3", "-1/5") // addition
+#q.sub("2/3", "1/4") // subtraction
+#q.mul("3/4", "2/3", "4/5") // multiplication
+#q.div("5/6", "3/2") // division
+#q.limit-den(calc.pi, 10000) // limiting maximum denominator
+#q.pow("3/2", 5) // raising to an integer power
+
+#q.to-str(q.from(113, 355)) // convert to string
+#q.to-math(q.from(113, 355)) // convert to formatted `math.equation` element
+```
+
+Currently, `rational.from` supports fraction notation and decimal notation with an optional set of [repeating digits](https://en.wikipedia.org/wiki/Repeating_decimal) enclosed in square brackets.
+
+```typ
+#import "@preview/peano:0.1.0"
+#import peano.number: rational as q
+
+// normal values
+
+#q.from("1/2")
+#q.from("-2/3") // sign before numerator
+#q.from("5/-4") // sign before denominator
+
+// infinity or indeterminate values
+
+#q.from("1/0")  // infinity
+#q.from("-1/0") // negative infinity
+#q.from("1/-0") // also negative infinity
+#q.from("0/0")  // NaN
+
+// decimal notation
+
+#q.from("0.25")
+#q.from("0.[3]") // repeating part wrapped in bracket
+#q.from("3.[142857]")
+#q.from("1.14[514]")
+#q.from("1[2.3]") // repeating part can cross decimal point
+```
+
+A rational number can be displayed in both string and math format by using the `rational.to-str` and `rational.to-math` methods.
+
+```typ
+#import "@preview/peano:0.1.0"
+#import peano.number: rational as q
+
+#let value = q.from(113, 355)
+
+#q.to-str(value)
+#q.to-math(value)
+```
+
+### Complex numbers
+
+```typ
+#import "@preview/peano:0.1.0"
+#import peano.number: complex as c
+
+#c.from("1+2i") // from string
+#c.from(3, 4) // from real and imaginary parts
+#c.add("1+2i", "3+4i", "-2+3i", "6-5i", "2i")
+```
+
+## Number theory
+
+The number theory sub module `peano.ntheory` currently supports prime factorization and the extended Euclidean algorithm that gives out the coefficients $u$ and $v$ in Bézout's identity $\gcd (a, b) = u a + v b$.
+
+## Mathematic functions
+
+The `peano.func` sub-module provides a collection of basic mathematic functions. Some of them are also included in Typst's `calc` module, but extended to support complex number input. Other self-defined functions also support function input if they can be defined in the complex field &#x210;.
+
+### Special functions
+
+The `peano.func.special` sub-module include special functions such as the gamma function, zeta function, Gauss error function.

packages/preview/peano/0.1.0/src/_impl/func/common.typ

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+// -> func/common.typ
+
+#import "init.typ": extend-calc-func-to-complex, define-func-with-complex, call-wasm-real-func, call-wasm-complex-func
+#import "../number/complex.typ" as c: complex, is-complex, make-complex
+#let math-utils-wasm = plugin("../math-utils.wasm")
+
+#let /*pub*/ exp = extend-calc-func-to-complex("exp")
+#let /*pub*/ ln(x) = {
+  if is-complex(x) {
+    call-wasm-complex-func(math-utils-wasm.ln_complex, x)
+  } else if x < 0 {
+    call-wasm-complex-func(math-utils-wasm.ln_complex, complex(x))
+  } else if x == 0 {
+    -float.inf
+  } else {
+    calc.ln(x)
+  }
+}
+
+#let log-complex(x, base: 10.0) = {
+  if base == 2 {
+    call-wasm-complex-func(math-utils-wasm.log2_complex, x)
+  } else if base == 10 {
+    call-wasm-complex-func(math-utils-wasm.log10_complex, x)
+  } else {
+    c.div(
+      call-wasm-complex-func(math-utils-wasm.ln_complex, x),
+      ln(base),
+    )
+  }
+}
+
+#let /*pub*/ log(x, base: 10.0) = {
+  if is-complex(x) {
+    log-complex(x, base: base)
+  } else if x < 0 {
+    log-complex(complex(x), base: base)
+  } else if x == 0 {
+    if is-complex(base) or base <= 0 {
+      c.nan
+    } else if base < 1 {
+      float.inf
+    } else if base == 1 {
+      float.nan
+    } else {
+      -float.inf
+    }
+  } else {
+    calc.log(x, base: base)
+  }
+}
+
+#let /*pub*/ sin = extend-calc-func-to-complex("sin")
+#let /*pub*/ cos = extend-calc-func-to-complex("cos")
+#let /*pub*/ tan = extend-calc-func-to-complex("tan")
+#let /*pub*/ sinh = extend-calc-func-to-complex("sinh")
+#let /*pub*/ cosh = extend-calc-func-to-complex("cosh")
+#let /*pub*/ tanh = extend-calc-func-to-complex("tanh")
+
+#let /*pub*/ asin(x) = {
+  if is-complex(x) {
+    call-wasm-complex-func(math-utils-wasm.asin_complex, x)
+  } else if x < -1 or x > 1 {
+    call-wasm-complex-func(math-utils-wasm.asin_complex, complex(x))
+  } else {
+    calc.asin(x)
+  }
+}
+
+#let /*pub*/ acos(x) = {
+  if is-complex(x) {
+    call-wasm-complex-func(math-utils-wasm.acos_complex, x)
+  } else if x < -1 or x > 1 {
+    call-wasm-complex-func(math-utils-wasm.acos_complex, complex(x))
+  } else {
+    calc.acos(x)
+  }
+}
+
+#let /*pub*/ atan = extend-calc-func-to-complex("atan")
+#let /*pub*/ asinh = define-func-with-complex("asinh")
+
+#let /*pub*/ acosh(x) = {
+  if x < 1 {
+    x = complex(x)
+  }
+  if is-complex(x) {
+    call-wasm-complex-func(math-utils-wasm.acosh_complex, x)
+  } else {
+    call-wasm-real-func(math-utils-wasm.atanh, x)
+  }
+}
+
+#let /*pub*/ atanh(x) = {
+  if x < -1 or x > 1 {
+    x = complex(x)
+  }
+  if is-complex(x) {
+    call-wasm-complex-func(math-utils-wasm.atanh_complex, x)
+  } else {
+    call-wasm-real-func(math-utils-wasm.atanh, x)
+  }
+}
+
+#let /*pub*/ abs(x) = {
+  if is-complex(x) {
+    let (re, im) = x
+    calc.norm(re, im)
+  } else {
+    calc.abs(x)
+  }
+}
+
+#let /*pub*/ arg(x) = {
+  if is-complex(x) {
+    let (re, im) = x
+    calc.atan2(re, im)
+  } else if x >= 0 {
+    0deg
+  } else {
+    180deg
+  }
+}

packages/preview/peano/0.1.0/src/_impl/func/init.typ

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+#import "../number/complex.typ" as c: complex, is-complex, make-complex
+#let math-utils-wasm = plugin("../math-utils.wasm")
+
+#let calc-funcs = dictionary(calc)
+#let math-utils-funcs = dictionary(math-utils-wasm)
+
+#let call-wasm-complex-func(complex-func, x) = {
+  let result-bytes = complex-func(
+      x.re.to-bytes(),
+      x.im.to-bytes(),
+    )
+    let re = float.from-bytes(result-bytes.slice(0, 8))
+    let im = float.from-bytes(result-bytes.slice(8))
+    make-complex(re, im)
+}
+
+#let call-wasm-real-func(real-func, x) = {
+  let x = if type(x) == angle {
+    x.rad()
+  } else {
+    float(x)
+  }
+  float.from-bytes(real-func(x.to-bytes()))
+}
+
+#let extend-calc-func-to-complex(func-name) = {
+  let real-func = calc-funcs.at(func-name)
+  let complex-func = math-utils-funcs.at(func-name + "_complex")
+  x => {
+    if is-complex(x) {
+      call-wasm-complex-func(complex-func, x)
+    } else {
+      let x = if type(x) == angle {
+        x.rad()
+      } else {
+        x
+      }
+      real-func(x)
+    }
+  }
+}
+
+#let define-func-with-complex(func-name) = {
+  let real-func = math-utils-funcs.at(func-name)
+  let complex-func = math-utils-funcs.at(func-name + "_complex")
+  x => {
+    if is-complex(x) {
+      call-wasm-complex-func(complex-func, x)
+    } else {
+      call-wasm-real-func(real-func, x)
+    }
+  }
+}
+
+#let define-func-2-with-complex(func-name) = {
+  let real-func = math-utils-funcs.at(func-name)
+  let complex-func = math-utils-funcs.at(func-name + "_complex")
+  (x1, x2) => {
+    if is-complex(x1) or is-complex(x2) {
+      let x1 = complex(x1)
+      let x2 = complex(x2)
+      let result-bytes = complex-func(
+        x1.re.to-bytes(),
+        x1.im.to-bytes(),
+        x2.re.to-bytes(),
+        x2.im.to-bytes(),
+      )
+      let re = float.from-bytes(result-bytes.slice(0, 8))
+      let im = float.from-bytes(result-bytes.slice(8))
+      make-complex(re, im)
+    } else {
+      let x1 = float(x1)
+      let x2 = float(x2)
+      float.from-bytes(real-func(x1.to-bytes(), x2.to-bytes()))
+    }
+  }
+}
+
+#let calc-funcs-with-complex = calc-funcs.keys().filter(it => (it + "_complex") in math-utils-funcs)
+#let extended-calc-funcs = calc-funcs-with-complex.map(it => (it, extend-calc-func-to-complex(it))).to-dict()
+

packages/preview/peano/0.1.0/src/_impl/func/special.typ

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+// -> func/special.typ
+/// Special mathematic functions.
+
+#import "init.typ": define-func-with-complex, define-func-2-with-complex
+
+/// The #link("https://en.wikipedia.org/wiki/Gamma_function")[$Gamma$ function],
+/// defined by $Gamma(z) = integral_0^oo t^(z - 1) upright(e)^(-t) dif t$.
+#let /*pub*/ gamma = define-func-with-complex("gamma")
+
+/// The #link("https://en.wikipedia.org/wiki/Digamma_function")[digamma function],
+/// which is the derivative of the logarithm of $Gamma$ function
+/// $psi(z) = dif/(dif z) ln Gamma(z) = (Gamma'(z))/(Gamma(z))$.
+#let /*pub*/ digamma = define-func-with-complex("digamma")
+
+/// same as `digamma`
+#let /*pub*/ psi = digamma
+
+/// The #link("https://en.wikipedia.org/wiki/Error_function")[Gauss error function],
+/// defined by $erf z = 2/sqrt(pi) integral_0^z e^(-t^2) dif t$
+#let /*pub*/ erf = define-func-with-complex("erf")
+
+/// #link("https://en.wikipedia.org/wiki/Riemann_zeta_function")[Riemann's $zeta$ function]
+/// defined by $zeta(s) = sum_(n = 1)^oo 1/(n^s)$ for $Re s > 1$ and its analytic continuation otherwise.
+#let /*pub*/ zeta = define-func-with-complex("zeta")
+
+/// The #link("https://en.wikipedia.org/wiki/Beta_function")[$Beta$ function],
+/// defined by $Beta(z_1, z_2) = integral_0^1 t^(z_1 - 1) (1 - t)^(z_2 - 1) dif t$.
+/// Equals to $(Gamma(z_1) Gamma(z_2))/(Gamma(z_1 + z_2))$
+#let /*pub*/ beta = define-func-2-with-complex("beta")
+
+// Euler's $gamma$ constant. Equals to $lim_(n -> oo) ((sum_(k = 1)^(n) 1/n) - ln n)$
+#let /*pub*/ euler-gamma = -digamma(1)

packages/preview/peano/0.1.0/src/_impl/ntheory.typ

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+// -> ntheory.typ
+/// number theory operations
+
+#let math-utils-wasm = plugin("math-utils.wasm")
+
+#let /*pub*/ prime-fac(num) = {
+  cbor(math-utils-wasm.prime_factors(num.to-bytes(endian: "little")))
+}
+
+/// Execute the extended Euclidean algorithm to find the greatest common devisor $d = gcd(a, b)$ for $a$ and $b$ with coefficients $u$, $v$ in Bézout's identity such that $d = u a + v b$. The return value is a triple $(d, u, v)$.
+#let /*pub*/ egcd(a, b) = {
+  cbor(
+    math-utils-wasm.extended_gcd(
+      a.to-bytes(endian: "little"),
+      b.to-bytes(endian: "little"),
+    )
+  )
+}