Symbolism-master C#计算库下载 -

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using Symbolism.Has;
using Symbolism.Trigonometric;
using Symbolism.CoefficientGpe;
using Symbolism.AlgebraicExpand;
using Symbolism.DegreeGpe;
namespace Symbolism.IsolateVariable
{
public static class Extensions
{
public static MathObject IsolateVariableEq(this Equation eq, Symbol sym)
{
if (eq.Operator == Equation.Operators.NotEqual) return eq;
if (eq.FreeOf(sym)) return eq;
// sin(x) / cos(x) == y -> tan(x) == y
if (eq.a is Product && (eq.a as Product).elts.Any(elt => elt == new Sin(sym)) &&
eq.a is Product && (eq.a as Product).elts.Any(elt => elt == 1 / new Cos(sym)))
return
(eq.a / new Sin(sym) * new Cos(sym) * new Tan(sym) == eq.b).IsolateVariableEq(sym);
// A sin(x)^2 == B sin(x) cos(x) -> A sin(x)^2 / (B sin(x) cos(x)) == 1
if (
eq.a is Product &&
(eq.a as Product).elts.Any(elt =>
(elt == new Sin(sym)) ||
((elt is Power) && (elt as Power).bas == new Sin(sym) && (elt as Power).exp is Number)) &&
eq.b is Product &&
(eq.b as Product).elts.Any(elt =>
(elt == new Sin(sym)) ||
((elt is Power) && (elt as Power).bas == new Sin(sym) && (elt as Power).exp is Number))
)
return
(eq.a / eq.b == 1).IsolateVariableEq(sym);
if (eq.b.Has(sym)) return IsolateVariableEq(new Equation(eq.a - eq.b, 0), sym);
if (eq.a == sym) return eq;
// (a x^2 + c) / x == - b
if (eq.a is Product &&
(eq.a as Product).elts.Any(
elt =>
elt is Power &&
(elt as Power).bas == sym &&
(elt as Power).exp == -1))
return IsolateVariableEq(eq.a * sym == eq.b * sym, sym);
//if (eq.a is Product &&
// (eq.a as Product).elts.Any(
// elt =>
// elt is Power &&
// (elt as Power).bas == sym &&
// (elt as Power).exp is Integer &&
// ((elt as Power).exp as Integer).val < 0))
// return IsolateVariableEq(eq.a * sym == eq.b * sym, sym);
// if (eq.a.Denominator() is Product &&
// (eq.a.Denominator() as Product).Any(elt => elt.Base() == sym)
//
//
// (x + y)^(1/2) == z
//
// x == -y + z^2 && z >= 0
if (eq.a is Power && (eq.a as Power).exp == new Integer(1) / 2)
return IsolateVariableEq((eq.a ^ 2) == (eq.b ^ 2), sym);
// 1 / sqrt(x) == y
if (eq.a is Power && (eq.a as Power).exp == -new Integer(1) / 2)
return (eq.a / eq.a == eq.b / eq.a).IsolateVariable(sym);
// x ^ 2 == y
// x ^ 2 - y == 0
if (eq.a.AlgebraicExpand().DegreeGpe(new List<MathObject>() { sym }) == 2 &&
eq.b != 0)
{
return
(eq.a - eq.b == 0).IsolateVariable(sym);
}
// a x^2 + b x + c == 0
if (eq.a.AlgebraicExpand().DegreeGpe(new List<MathObject>() { sym }) == 2)
{
var a = eq.a.AlgebraicExpand().CoefficientGpe(sym, 2);
var b = eq.a.AlgebraicExpand().CoefficientGpe(sym, 1);
var c = eq.a.AlgebraicExpand().CoefficientGpe(sym, 0);
if (a == null || b == null || c == null) return eq;
return new Or(
new And(
sym == (-b + (((b ^ 2) - 4 * a * c) ^ (new Integer(1) / 2))) / (2 * a),
(a != 0).Simplify()
).Simplify(),
new And(
sym == (-b - (((b ^ 2) - 4 * a * c) ^ (new Integer(1) / 2))) / (2 * a),
(a != 0).Simplify()
).Simplify(),
new And(sym == -c / b, a == 0, (b != 0).Simplify()).Simplify(),
new And(
(a == 0).Simplify(),
(b == 0).Simplify(),
(c == 0).Simplify()
).Simplify()
).Simplify();
}
// (x + y == z).IsolateVariable(x)
if (eq.a is Sum && (eq.a as Sum).elts.Any(elt => elt.FreeOf(sym)))
{
var items = ((Sum)eq.a).elts.FindAll(elt => elt.FreeOf(sym));
//return IsolateVariable(
// new Equation(
// eq.a - new Sum() { elts = items }.Simplify(),
// eq.b - new Sum() { elts = items }.Simplify()),
// sym);
//var new_a = eq.a; items.ForEach(elt => new_a = new_a - elt);
//var new_b = eq.b; items.ForEach(elt => new_b = new_b - elt);
var new_a = new Sum() { elts = (eq.a as Sum).elts.Where(elt => items.Contains(elt) == false).ToList() }.Simplify();
var new_b = eq.b; items.ForEach(elt => new_b = new_b - elt);
// (new_a as Sum).Where(elt => items.Contains(elt) == false)
return IsolateVariableEq(new Equation(new_a, new_b), sym);
//return IsolateVariable(
// new Equation(
// eq.a + new Sum() { elts = items.ConvertAll(elt => elt * -1) }.Simplify(),
// eq.b - new Sum() { elts = items }.Simplify()),
// sym);
}
// a b + a c == d
// a + a c == d
if (eq.a is Sum && (eq.a as Sum).elts.All(elt => elt.DegreeGpe(new List<MathObject>() { sym }) == 1))
{
//return
// (new Sum() { elts = (eq.a as Sum).elts.Select(elt => elt / sym).ToList() }.Simplify() == eq.b / sym)
// .IsolateVariable(sym);
return
(sym * new Sum() { elts = (eq.a as Sum).elts.Select(elt => elt / sym).ToList() }.Simplify() == eq.b)
.IsolateVariable(sym);
}
// -sqrt(x) + z * x == y
if (eq.a is Sum && eq.a.Has(sym ^ (new Integer(1) / 2))) return eq;
// sqrt(a + x) - z * x == -y
if (eq.a is Sum && eq.a.Has(elt => elt is Power && (elt as Power).exp == new Integer(1) / 2 && (elt as Power).bas.Has(sym)))
return eq;
if (eq.a is Sum && eq.AlgebraicExpand().Equals(eq)) return eq;
if (eq.a is Sum) return eq.AlgebraicExpand().IsolateVariable(sym);
// (x + 1) / (x + 2) == 3
if (eq.a.Numerator().Has(sym) && eq.a.Denominator().Has(sym))
{
return IsolateVariableEq(eq.a * eq.a.Denominator() == eq.b * eq.a.Denominator(), sym);
}
// sqrt(2 + x) * sqrt(3 + x) == y
if (eq.a is Product && (eq.a as Product).elts.All(elt => elt.Has(sym))) return eq;
if (eq.a is Product)
{
var items = ((Product)eq.a).elts.FindAll(elt => elt.FreeOf(sym));
return IsolateVariableEq(
new Equation(
eq.a / new Product() { elts = items }.Simplify(),
eq.b / new Product() { elts = items }.Simplify()),
sym);
}
// x ^ -2 == y
if (eq.a is Power &&
(eq.a as Power).bas == sym &&
(eq.a as Power).exp is Integer &&
((eq.a as Power).exp as Integer).val < 0)
return (eq.a / eq.a == eq.b / eq.a).IsolateVariableEq(sym);
if (eq.a is Power) return eq;
// sin(x) == y
// Or(x == asin(y), x == Pi - asin(y))
if (eq.a is Sin)
return
new Or(
(eq.a as Sin).args[0] == new Asin(eq.b),
(eq.a as Sin).args[0] == new Symbol("Pi") - new Asin(eq.b))
.IsolateVariable(sym);
// tan(x) == y
// x == atan(t)
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