MathAction new pages

ExampleTrigonometricConstants

Mon, 02 Mar 2026 18:17:05 +0000

Example of computations with trigonometric constants

HowToContribute

Wed, 08 Jan 2025 13:45:11 +0000

How to contribute

ExampleExtrema

Mon, 18 Nov 2024 13:07:09 +0000

We would like to find extrama of $x^2 + y^2 − 2x + 4y + 5$ on the curve with equation $2x^4 + 3y^7 = 4$. We set up and solve system of equations for Lagrange's multipliers: \begin{axiom} f := x^2 + y^2 - 2*x + 4*y + 5 g := 2*x^4 + 3*y^7 - 4 dfx := D(f, x) - l*D(g,x) dfy := D(f, y) - l*D(g, y) )set output tex off )set output algebra on r1 := solve([g, dfx, dfy], 1.0e-15) \end{axiom}

ExampleIntegration2

Mon, 02 Sep 2024 16:09:58 +0000

Here we show how FriCAS can help solving calculus problems. Task is: find integer n, $60 < n < 100$ such that x^n/(x^120 - 1) has simple integral.

Root denesting

Fri, 12 Jan 2024 14:31:01 +0000

FriCAS can denest many nested roots. This is implemented in an extra package so befor use we need to expose it: \begin{axiom} )expose RootSimplification \end{axiom}

FriCASProgrammingModel

Thu, 09 Nov 2023 16:00:08 +0000

FriCAS language (both interpreter and Spad) is imperative, basic operation is an assignment like \begin{axiom} a : Integer := 5 b : Integer := a + 2 \end{axiom} FriCAS language is typed, each variable and expression have type, assigned value must have correct type. Above we explicitly declared 'a' and 'b' to be of type 'Integer'. In same cases FriCAS can infer the correct type and allows use of variables without explicit declaration. Interpreter tries to assign reasonable type guessing user intent. Remark: this is quite different than type inference present in same languages.

ExampleInequalitiesViaCAD

Sat, 23 Sep 2023 12:40:58 +0000

Recenty in sci.math.symbolic there was a question if \begin{equation} b^2 \geq (a - c)^2 \end{equation} and \begin{equation} a^2 \geq b^2 \end{equation} implies \begin{equation} c^2 \geq (a + b)^2 \end{equation} or \begin{equation} c^2 \geq (a - b)^2. \end{equation}

ExampleCompositeFunction

Sat, 23 Sep 2023 01:04:28 +0000

In practice we frequently need to deal with composite functions. This is frequently formulated as 'y' depends in 'x' where 'x' is a function (say of argument 't'). Unlike some other systems in FriCAS one have to be explicit with dependencies. This make simple cases slightly more verbose, but allows clean handling of more complicated cases. For concretness consider the following situation: \begin{latex} $$ z(y(x(t))) $$ \end{latex} where 'z' is simple function of 'y', 'x' is simple function of 't' say \begin{latex} $$ z = c x y, $$ $$ x = \frac{1}{t} $$ \end{latex} and 'y' is arbitrary. We want to compute second derivative of our function.

ExampleSolve2

Fri, 22 Sep 2023 14:46:31 +0000

The following example appeared in Maxima mailing list (Maxima could not do it). Here we solve it using FriCAS. First we form system of equations: \begin{axiom} -- Form system of equations eqn1 := a1*x1^5 + a2*x2^5 + a3*x3^5 = 1 / 6 eqn2 := a1*x1^4 + a2*x2^4 + a3*x3^4 = 1 / 5 eqn3 := a1*x1^3 + a2*x2^3 + a3*x3^3 = 1 / 4 eqn4 := a1*x1^2 + a2*x2^2 + a3*x3^2 = 1 / 3 eqn5 := a1*x1 + a2*x2 + a3*x3 = 1 / 2 eqn6 := a1 + a2 + a3 = 1 eqns := [eqn1, eqn2, eqn3, eqn4, eqn5, eqn6]; \end{axiom}

GeneratingCompiledFunctions

Mon, 06 Jun 2022 15:01:33 +0000

Computing value of following polynomial was proposed as a benchmark: \begin{axiom} p := x^24+32*x^21+9*x^18+34*x^12+34*x^10+45*x^3 \end{axiom}