11 Apr 2026

Maxima Tables and Loops

Structured tabular output, 2-D display, and matrix construction using lists and loops in Maxima.

maxima io

Maxima supports disciplined, readable computational workflows by combining list generation, matrix constructors, and loop-based iteration with formatted printing. In practice, tabular output is produced with print(a, b, c) or printf(true, “format”, args), while symbolic objects can be displayed in Maxima’s two-dimensional mathematical form via the ~m format directive.

Tabular-style Output and 2-D Pretty Display

For line-by-line tabular output, print is sufficient for quick inspection, whereas printf provides precise control over alignment, numeric formatting, and line breaks. When the goal is to display an expression in Maxima’s 2-D mathematical form, use printf(true, “~m~%”, expr).

print(a, b, c); prints items in sequence.
printf(true, “format”, args); prints formatted output.
printf(true, “~m~%”, expr); prints an expression in Maxima’s 2-D mathematical display form.

for n:0 thru 5 do
    printf(true, "n = ~d   value = ~d~%", n, n^2);

Matrices and Programmatic Construction

Matrices can be created explicitly from row lists, or built from generated rows. The constructors matrix([row1], [row2], …), ident(n), and zeromatrix(m, n) provide a direct entry point for linear-algebra workflows, while list generators and loops allow formula-driven construction.

matrix([row1], [row2], …); creates a matrix from row lists.
ident(n); creates the identity matrix of order $n$.
zeromatrix(m, n); creates an $m \times n$ zero matrix.

A : matrix([1, 2], [3, 4]);
B : ident(2);
C : zeromatrix(2, 3);

A standard pattern is to generate each row as a list, then assemble the rows into a matrix:

M : matrix(
        makelist(i, i, 1, 3),
        makelist(i^2, i, 1, 3),
        makelist(i^3, i, 1, 3)
     );

\[\begin{pmatrix} 1 & 2 & 3 \\ 1 & 4 & 9 \\ 1 & 8 & 27 \end{pmatrix}\]

Lists with makelist and Iteration with for … do

List generation is central for building structured data prior to matrix conversion. The constructor makelist(expr, i, a, b) generates a list by evaluating expr as the index i ranges from a to b. Iteration is typically expressed using for i:1 thru n do expr;, and nested loops are natural for producing indexed output such as matrix-entry reports.

makelist(expr, i, a, b); generates a list over an index range.
for i:1 thru n do expr; iterates with integer stepping.
for i from a thru b do expr; equivalent explicit-range loop form.

L1 : makelist(i^2, i, 1, 5);
L2 : makelist(sin(k), k, 0, 4);

for i:1 thru 5 do print(i, i^2);

for i:1 thru 3 do
  for j:1 thru 3 do
    printf(true, "a[~d,~d] = ~d~%", i, j, i+j);

Minimal Working Session

kill(all)$

/* tabular-style output */
for n:1 thru 5 do
    printf(true, "n = ~d   n^2 = ~d~%", n, n^2)$

/* list generation */
L : makelist(k^2, k, 1, 4)$
print(L)$

/* matrix construction */
M : matrix(
      makelist(i, i, 1, 4),
      makelist(i^2, i, 1, 4)
    )$
print(M)$
printf(true, "~m~%", M)$