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TaylorTerms(AngouriMath.Entity,System.ValueTuple{AngouriMath.Entity.Variable,AngouriMath.Entity.Variable,AngouriMath.Entity}[])

Method (no overloads)

Summary

Finds the symbolic expression of terms of the Taylor expansion of the given function,
https://en.wikipedia.org/wiki/Taylor_series

Do NOT call ToArray() or anything like this on the result of this method. It is
infinite iterator. To get a finite result as in a sum of finite number of terms,
call TaylorExpansion

Parameter "expr"

The function to find the Taylor expansion of

Parameter "exprToPolyVars"

The variable/s to take the series over, the variable the series will be over,
and the variable values at which the Taylor polynomial will be found
(e. g. if you want to find the taylor polynomial of Sin("t") around t=1, and want
n to take that place in the series, then you may want to use ("t","n","1") for this argument)

Returns

An infinite iterator over the terms of Taylor series of the given expression.

Example

using AngouriMath;
using System;
using System.Linq;
using static AngouriMath.MathS;
using static AngouriMath.MathS.Series;

var (x, y) = MathS.Var("x", "y");
Console.WriteLine(Sin(x));
Console.WriteLine(Maclaurin(Sin(x), 1, x));
Console.WriteLine(Maclaurin(Sin(x), 2, x));
Console.WriteLine(Maclaurin(Sin(x), 3, x));
Console.WriteLine(Maclaurin(Sin(x), 4, x));
Console.WriteLine(Maclaurin(Sin(x), 10, x).Simplify());
Console.WriteLine("----------------------");
var expr = Sin(x) + Cos(y);
Console.WriteLine(expr);
Console.WriteLine(Maclaurin(expr, 6, x, y).Simplify());
Console.WriteLine("----------------------");
Console.WriteLine(expr);
Console.WriteLine(Taylor(expr, 6, (x, 1)));
Console.WriteLine("----------------------");
Console.WriteLine(expr);
Console.WriteLine(Taylor(expr, 6, (x, 1), (y, 5)));
Console.WriteLine("----------------------");
Console.WriteLine(expr);
Console.WriteLine(Taylor(expr, 6, (x, "z_1", 1), (y, "z_2", 5)));
Console.WriteLine("----------------------");
var first3Terms = 
    TaylorTerms(expr, (x, x, 0), (y, y, 1))
    .Take(3);
var first6Terms =
    TaylorTerms(expr, (x, x, 0), (y, y, 1))
    .Take(6);
foreach (var term in first6Terms)
    Console.WriteLine($"Received {term}");

Prints

sin(x)
0
0 + x
0 + x + 0
0 + x + 0 + -x ^ 3 / 3!
x ^ 9 / 362880 - x ^ 7 / 5040 + x ^ 5 / 120 - x ^ 3 / 6 + x
----------------------
sin(x) + cos(y)
1 + (6 * x ^ 5 - 120 * x ^ 3) / 720 + x + (2 * y ^ 4 - 24 * y ^ 2) / 48
----------------------
sin(x) + cos(y)
sin(1) + cos(y) + cos(1) * (x - 1) + -sin(1) * (x - 1) ^ 2 / 2! + cos(1) * (-1) * (x - 1) ^ 3 / 3! + -sin(1) * (-1) * (x - 1) ^ 4 / 4! + cos(1) * (-1) * (-1) * (x - 1) ^ 5 / 5!
----------------------
sin(x) + cos(y)
sin(1) + cos(5) + cos(1) * (x - 1) + -sin(5) * (y - 5) + (-sin(1) * (x - 1) ^ 2 + cos(5) * (-1) * (y - 5) ^ 2) / 2! + (cos(1) * (-1) * (x - 1) ^ 3 + -sin(5) * (-1) * (y - 5) ^ 3) / 3! + (-sin(1) * (-1) * (x - 1) ^ 4 + cos(5) * (-1) * (-1) * (y - 5) ^ 4) / 4! + (cos(1) * (-1) * (-1) * (x - 1) ^ 5 + -sin(5) * (-1) * (-1) * (y - 5) ^ 5) / 5!
----------------------
sin(x) + cos(y)
sin(1) + cos(5) + cos(1) * (z_1 - 1) + -sin(5) * (z_2 - 5) + (-sin(1) * (z_1 - 1) ^ 2 + cos(5) * (-1) * (z_2 - 5) ^ 2) / 2! + (cos(1) * (-1) * (z_1 - 1) ^ 3 + -sin(5) * (-1) * (z_2 - 5) ^ 3) / 3! + (-sin(1) * (-1) * (z_1 - 1) ^ 4 + cos(5) * (-1) * (-1) * (z_2 - 5) ^ 4) / 4! + (cos(1) * (-1) * (-1) * (z_1 - 1) ^ 5 + -sin(5) * (-1) * (-1) * (z_2 - 5) ^ 5) / 5!
----------------------
Received cos(1)
Received x + -sin(1) * (y - 1)
Received cos(1) * (-1) * (y - 1) ^ 2 / 2!
Received (-x ^ 3 + -sin(1) * (-1) * (y - 1) ^ 3) / 3!
Received cos(1) * (-1) * (-1) * (y - 1) ^ 4 / 4!
Received (x ^ 5 + -sin(1) * (-1) * (-1) * (y - 1) ^ 5) / 5!

AngouriMath

Table of contents

AngouriMath

TaylorTerms​(AngouriMath.​Entity,​System.​ValueTuple{AngouriMath.​Entity.​Variable,​AngouriMath.​Entity.​Variable,​AngouriMath.​Entity}[])

TaylorTerms(AngouriMath.Entity,System.ValueTuple{AngouriMath.Entity.Variable,AngouriMath.Entity.Variable,AngouriMath.Entity}[])