RREFMOD

Type:

Command

Description:

Performs modular row-reduction to echelon form on a matrix, modulo the current modulus.

Access:

Catalog, …µ

Input:

A matrix.

Output:

The modular row-reduced matrix. The modulo value is set using the Modes CAS input form.

Flags:

Exact mode must be set (flag –105 clear).

 

Numeric mode must not be set (flag –3 clear).

 

If flag –126 is clear (the default), row reduction is done with the last column. If the flag is set, row

 

reduction is done without reducing the last column, but the last column will be modified by the

 

reduction of the rest of the matrix.

Example:

Reduce to row-reduced echelon form, modulo 3, the matrix:

 

 

2

1

 

Command:

 

 

3 4

 

 

rref[[2,1][3,4]]

Result:

[[-1,0][0,1]]

See also:

rref

 

 

 

RRK

Command

Type:

Description:

Solve for Initial Values (Rosenbrock, Runge–Kutta) Command: Computes the solution to an

 

initial value problem for a differential equation with known partial derivatives.

 

RRK solves y'(t) = f(t,y), where y(t0) = y0. The arguments and results are as follows:

 

 

{ list } contains five items in this order:

 

 

 

– The independent variable (t).

 

 

 

– The solution variable (y).

 

 

 

– The right-hand side of the differential equation (or a variable where the expression is stored).

 

 

 

– The partial derivative of y'(t) with respect to the solution variable (or a variable where the

 

 

 

 

expression is stored).

 

 

 

– The partial derivative of y'(t) with respect to the independent variable (or a variable where the

 

 

 

 

expression is stored).

 

 

xtol sets the tolerance value. If a list is used, the first value is the tolerance and the second value

 

 

 

is the initial candidate step size.

 

 

xTfinal specifies the final value of the independent variable.

 

 

 

RRK repeatedly calls RKFSTEP as its steps from the initial value to xTfinal.

Access:

…µRRK

 

 

 

 

 

Input/Output:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

L3/A1

L2/A2

L1/A3

 

L2/I1

L1/I2

 

 

 

 

 

 

 

 

 

 

{ list }

xtol

xT final

{ list }

xtol

 

 

{ list }

{ xtol xhstep }

xT final

 

{ list }

xtol

 

 

 

 

 

 

 

 

 

 

L = Level; A = Argument; I = item

 

 

 

Example: Solve the following initial value problem for y(8), given that y(0) = 0:

 

 

 

1

 

2

 

y

= 1

+ t2

− 2y

 

= f (t, y)

 

 

Full Command and Function Reference 3-211