Reference Guide
Full Command and Function Reference 3-211
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
3
4
Command:
rref[[2,1][3,4]]
Result:
[[-1,0][0,1]]
See also: rref
RRK
Type: Command
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(t
0
) = y
0
. 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).
•
x
tol
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.
•
x
Tfinal
specifies the final value of the independent variable.
RRK repeatedly calls RKFSTEP as its steps from the initial value to x
Tfinal
.
Access: …µ
RRK
Input/Output:
L
3
/A
1
L
2
/A
2
L
1
/A
3
L
2
/I
1
L
1
/I
2
{ list }
x
tol
x
T final
→
{ list }
x
tol
{ list }
{ x
tol
x
hstep
}
x
T final
{ list }
x
tol
L = Level; A = Argument; I = item
Example: Solve the following initial value problem for y(8), given that y(0) = 0:
),(2
1
1
2
2
ytfy
t
y =−
+
=
′