CTAN sync 202211060301

1 files changed, 241 insertions, 0 deletions

diff --git a/macros/luatex/latex/luacas/tex/algebra/rational.lua b/macros/luatex/latex/luacas/tex/algebra/rational.lua
new file mode 100644
index 0000000000..811909a948
--- /dev/null
+++ b/macros/luatex/latex/luacas/tex/algebra/rational.lua
@@ -0,0 +1,241 @@
+--- @class Rational
+--- Represents an element of the field of rational numbers or rational functions.
+--- @field numerator Ring
+--- @field denominator Ring
+--- @field ring RingIdentifier
+Rational = {}
+__Rational = {}
+
+
+--------------------------
+-- Static functionality --
+--------------------------
+
+-- Metatable for ring objects.
+local __obj = {__index = Rational, __eq = function(a, b)
+    return a["ring"] == b["ring"] and
+            (a["child"] == b["child"] or a["child"] == nil or b["child"] == nil) and
+            (a["symbol"] == b["symbol"] or a["child"] == nil or b["child"] == nil)
+end, __tostring = function(a)
+        if a.symbol then
+            return tostring(a.child.child) .. "(" .. a.symbol .. ")"
+        end
+        if a.child then
+            return "QQ"
+        end
+        return "(Generic Fraction Field)"
+    end}
+
+--- @param symbol SymbolExpression
+--- @param child RingIdentifier
+--- @return RingIdentifier
+function Rational.makering(symbol, child)
+    local t = {ring = Rational}
+    t.symbol = symbol
+    t.child = child
+    t = setmetatable(t, __obj)
+    return t
+end
+
+--- Converts a string of the form -?[0-9]+ or -?[0-9]+\/[0-9]+ to a rational number.
+--- @param str string
+--- @return Rational|Integer
+function Rational.fromstring(str)
+    local divloc = string.find(str, "/");
+    if not divloc then
+        return Integer(str)
+    end
+    return Rational(Integer(string.sub(str, 1, divloc - 1)), Integer(string.sub(str, divloc + 1, #str)))
+end
+
+
+----------------------------
+-- Instance functionality --
+----------------------------
+
+-- So we don't have to copy the field operations each time.
+local __o = Copy(__FieldOperations)
+__o.__index = Rational
+__o.__tostring = function(a)
+    if a.ring.symbol then
+        return "(" .. tostring(a.numerator)..")/("..tostring(a.denominator) .. ")"
+    end
+    return tostring(a.numerator).."/"..tostring(a.denominator)
+end
+
+--- Creates a new rational given a numerator and denominator that are part of the same ring.
+--- Rational numbers are represented uniquely.
+--- @param n Ring
+--- @param d Ring
+--- @param keep boolean
+function Rational:new(n, d, keep)
+    local o = {}
+    o = setmetatable(o, __o)
+
+    if n:getring() == PolynomialRing.getring() then
+        o.symbol = n.symbol
+    end
+
+    if d:getring() == PolynomialRing.getring() then
+        o.symbol = d.symbol
+    end
+
+    if d == Integer(0) then
+        error("Arithmetic error: division by zero")
+    end
+
+    n = n or Integer.zero()
+    d = d or Integer.one()
+    o.numerator = n
+    o.denominator = d
+    o:reduce()
+
+    if (not keep) and o.denominator == Integer.one() or (not keep) and o.numerator == Integer.zero() then
+        return o.numerator
+    end
+
+    return o
+end
+
+--- Reduces a rational expression to standard form. This method mutates its object.
+function Rational:reduce()
+    if self.numerator:getring() == Integer.getring() then
+        if self.denominator < Integer.zero() then
+            self.denominator = -self.denominator
+            self.numerator = -self.numerator
+        end
+        local gcd = Integer.gcd(self.numerator, self.denominator)
+        self.numerator = self.numerator//gcd
+        self.denominator = self.denominator//gcd
+        self.ring = Integer.getring()
+    elseif self.numerator:getring() == PolynomialRing.getring() then
+        local lc = self.denominator:lc()
+        self.denominator = self.denominator/lc
+        self.numerator = self.numerator/lc
+        local gcd = PolynomialRing.gcd(self.numerator, self.denominator)
+        self.numerator = self.numerator//gcd
+        self.denominator = self.denominator//gcd
+        self.ring = Ring.resultantring(self.numerator:getring(), self.denominator:getring())
+    end
+end
+
+
+--- @return RingIdentifier
+function Rational:getring()
+    local t = {ring=Rational}
+    if self then
+        t.child = self.ring
+        t.symbol = self.symbol
+    end
+    t = setmetatable(t, __obj)
+    return t
+end
+
+--- @param ring RingIdentifier
+--- @return Ring
+function Rational:inring(ring)
+    if ring == self:getring() then
+        return self
+    end
+
+    if ring == Rational:getring() and ring.symbol then
+        if not self:getring().symbol then
+            return Rational(self:inring(ring.child), self:inring(ring.child):one(), true)
+        end
+        return Rational(self.numerator:inring(ring.child), self.denominator:inring(ring.child), true)
+    end
+
+    if ring == PolynomialRing:getring() then
+        return PolynomialRing({self:inring(ring.child)}, ring.symbol)
+    end
+
+    error("Unable to convert element to proper ring.")
+end
+
+--- @return boolean
+function Rational:isconstant()
+    if self.symbol then
+        return false
+    end
+    return true
+end
+
+--- @return Expression
+function Rational:tocompoundexpression()
+    return BinaryOperation(BinaryOperation.DIV, {self.numerator:tocompoundexpression(), self.denominator:tocompoundexpression()})
+end
+
+--- Returns this rational as a floating point number. Can only approximate the value of most rationals.
+--- @return number
+function Rational:asnumber()
+    return self.numerator:asnumber() / self.denominator:asnumber()
+end
+
+function Rational:add(b)
+    return Rational(self.numerator * b.denominator + self.denominator * b.numerator, self.denominator * b.denominator)
+end
+
+function Rational:neg()
+    return Rational(-self.numerator, self.denominator, true)
+end
+
+function Rational:mul(b)
+    return Rational(self.numerator * b.numerator, self.denominator * b.denominator)
+end
+
+-- function Rational:inv(b)
+--     return Rational(self.numerator * b.numerator, self.denominator * b.denominator)
+-- end
+
+function Rational:pow(b)
+    return (self.numerator ^ b) / (self.denominator ^ b)
+end
+
+function Rational:div(b)
+    return Rational(self.numerator * b.denominator, self.denominator * b.numerator)
+end
+
+function Rational:eq(b)
+    return self.numerator == b.numerator and self.denominator == b.denominator
+end
+
+function Rational:lt(b)
+    if self.numerator < Integer.zero() and b.numerator > Integer.zero() then
+        return true
+    end
+    if self.numerator > Integer.zero() and b.numerator < Integer.zero() then
+        return false
+    end
+
+    if (self.numerator >= Integer.zero() and b.numerator >= Integer.zero()) or (self.numerator <= Integer.zero() and b.numerator <= Integer.zero()) then
+        return self.numerator * b.denominator < self.denominator * b.numerator
+    end
+    return self.numerator * b.denominator > self.denominator * b.numerator
+end
+
+function Rational:le(b)
+    return self:eq(b) or self:lt(b)
+end
+
+function Rational:zero()
+    return Integer.zero()
+end
+
+function Rational:one()
+    return Integer.one()
+end
+
+function Rational:tolatex()
+    if string.sub(self.numerator:tolatex(),1,1) == '-' then
+        return "- \\frac{" .. string.sub(self.numerator:tolatex(),2,-1) .. "}{" .. self.denominator:tolatex() .. "}"
+    end
+    return "\\frac{" .. self.numerator:tolatex() .."}{".. self.denominator:tolatex().. "}"
+end
+
+-----------------
+-- Inheritance --
+-----------------
+
+__Rational.__index = Field
+__Rational.__call = Rational.new
+Rational = setmetatable(Rational, __Rational)
\ No newline at end of file