Symbolic

Full name Microsoft.VisualBasic.Math.Lambda.Symbolic.Symbolic Assembly Microsoft.VisualBasic.Math.Lambda Members 23

symbolic computation engine

01 Syntax

Microsoft.VisualBasic.Math.Lambda.Symbolic.Symbolic

02 Methods

Name	Overloads	Summary
Rationalize	2	Rationalise the expression (string form overload).
Substitute	2	Simultaneously replace symbols by the expressions parsed from mapping.
Derivative	1	First derivative of expr with respect to x.
DerivativeN	1	The n-th order derivative of expr with respect to x.
PartialDerivative	1	Partial derivative of a (possibly multivariate) expression with respect to x.
Jacobian	1	Jacobian matrix of a vector valued function F with respect to the variables.
Hessian	1	Hessian matrix of a scalar function f with respect to the variables.
ImplicitDerivative	1	Implicit derivative dy/dx for an equation F(x, y) = 0.
Integrate	1	Indefinite integral of expr with respect to var.
DefiniteIntegral	1	Definite integral of expr over [lower, upper].
Limit	1	Compute lim_{var -> target} expr.
Taylor	1	Taylor expansion of expr about point up to order.
TaylorWithRemainder	2	Taylor expansion together with its Lagrange remainder.
Factor	3	Factor a (possibly multivariate) polynomial over the explicitly given variable set.
TruthTable	1	Enumerate the truth table of a boolean function and return the minterms where it is true.
QuineMcCluskey	1	Quine-McCluskey minimisation, returning the prime implicants as 0/1/- strings.
QMCSimplifySOP	1	Minimal Sum-Of-Products of a boolean function.
QMCSimplifyPOS	1	Minimal Product-Of-Sums of a boolean function.

03 Members

method Rationalize overload 2 #

Rationalize(String)

Rationalise the expression: remove square roots and the imaginary unit from every denominator by conjugate multiplication, e.g. 1/(1 + sqrt(2)) -> sqrt(2) - 1, 1/(a + bi) -> (a - bi)/(a^2 + b^2).

method Rationalize #

Rationalize(Expression)

Rationalise the expression (string form overload).

method Substitute overload 2 #

Substitute(Expression, String, String)

Replace every occurrence of the symbol oldSymbol by the expression parsed from replacement.

method Substitute #

Substitute(Expression, Dictionary(Of String, String))

Simultaneously replace symbols by the expressions parsed from mapping.

method Derivative #

Derivative(String, String)

First derivative of expr with respect to x.

method DerivativeN #

DerivativeN(String, String, Int32)

The n-th order derivative of expr with respect to x.

method PartialDerivative #

PartialDerivative(String, String)

Partial derivative of a (possibly multivariate) expression with respect to x.

method Jacobian #

Jacobian(Expression(), String())

Jacobian matrix of a vector valued function F with respect to the variables.

method Hessian #

Hessian(Expression, String())

Hessian matrix of a scalar function f with respect to the variables.

method ImplicitDerivative #

ImplicitDerivative(Expression, String, String)

Implicit derivative dy/dx for an equation F(x, y) = 0. Returns -Fx / Fy.

method Integrate #

Integrate(String, String)

Indefinite integral of expr with respect to var.

method DefiniteIntegral #

DefiniteIntegral(String, String, Double, Double)

Definite integral of expr over [lower, upper].

method Limit #

Limit(String, String, String)

Compute lim_{var -> target} expr.

method Taylor #

Taylor(String, String, String, Int32)

Taylor expansion of expr about point up to order.

method TaylorWithRemainder overload 2 #

TaylorWithRemainder(String, String, String, Int32)

Taylor expansion together with its Lagrange remainder.

method TaylorWithRemainder #

TaylorWithRemainder(Expression, String, Expression, Int32)

Taylor expansion together with its Lagrange remainder.

method Factor overload 2 #

Factor(String, String)

Factorise a univariate polynomial expression (heuristic).

method Factor overload 3 #

Factor(String, String())

Factor a (possibly multivariate) polynomial over the explicitly given variable set, e.g. x^2 - y^2 -> (x - y) * (x + y).

method Factor #

Factor(Expression, String())

Factor a (possibly multivariate) polynomial over the explicitly given variable set.

method TruthTable #

TruthTable(String(), Func(Of Boolean(), Boolean))

Enumerate the truth table of a boolean function and return the minterms where it is true.

method QuineMcCluskey #

QuineMcCluskey(String(), Int32(), Int32())

Quine-McCluskey minimisation, returning the prime implicants as 0/1/- strings.

method QMCSimplifySOP #

QMCSimplifySOP(String(), Int32(), Int32())

Minimal Sum-Of-Products of a boolean function.

method QMCSimplifyPOS #

QMCSimplifyPOS(String(), Int32(), Int32())

Minimal Product-Of-Sums of a boolean function.