Re: [Maxima-discuss] [Maxima-bugs] [maxima:bugs] #4637 error partition_set

[Stavros M. <mac...@gm...>]

I hope it's clearer now how to use *integer_partitions*.

As for your original syntax, partition_set(...,length(list)=*2)*, Maxima
doesn't set *list* (or any other variable) to the candidate partition --
you'd need to write an explicit lambda-expression.

Here is a little introduction to the magic variables in Maxima written by
Gemini:

Maxima has several "magical" system variables which are implicitly set by
> Maxima as side effects of functions or to track interaction history.
>
> Here are the most notable ones, categorized by their behavior:
>
> 1. The "Context" Variables (Like piece)
>
> These are variables that are bound temporarily during the execution of a
> specific function or rule.
>
>    -
>
>    *piece*:
>    -
>
>       *Context:* Used inside substpart and substinpart.
>       -
>
>       *Magic:* It refers to the specific sub-expression currently being
>       replaced.
>       -
>
>       *Example:* substpart(piece^2, x+y+z, 2) replaces y with y^2.
>
> piece is unique because it captures a *context-dependent value during
execution* (specifically inside substpart),


>    -
>
>    *Pattern Matching Variables*:
>    -
>
>       *Context:* Used in defmatch, defrule, tellsimp, and let.
>       -
>
>       *Magic:* When you define a pattern with matchdeclare(x, predicate),
>       the variable x is automatically bound to the matching part of the
>       expression when the rule executes.
>       -
>
>       *Example:* If you define matchdeclare(a, true) and a rule for a^2,
>       when the rule matches (x+1)^2, the variable a is momentarily bound
>       to x+1 inside the rule's body.
>
> 2. The "Side-Effect" Variables (Set by specific functions)
>
> Unlike piece, these variables persist *after* a command is finished. They
> are often used to inspect "how" a problem was solved or to get details that
> didn't fit in the main return value.
>
>    -
>
>    *multiplicities*:
>    -
>
>       *Context:* Set by solve and allroots.
>       -
>
>       *Magic:* It becomes a list of integers corresponding to the
>       multiplicity of each solution returned.
>       -
>
>       *Example:*
>       Maxima
>
>       solve((x-1)^2 * (x-2) = 0, x);/* Returns [x=1, x=2] */multiplicities;/* Returns [2, 1] */
>
>       -
>
>    *method* (and friends in ode2):
>    -
>
>       *Context:* Set by ode2 (the ordinary differential equation solver).
>       -
>
>       *Magic:* After solving an ODE, method is set to the name of the
>       method Maxima used (e.g., linear, separable, exact).
>       -
>
>       *Related Variables:*
>       -
>
>          intfactor: Set to the integrating factor used (if any).
>
>          -
>
>          odeindex: Set to the index for Bernoulli or Euler equations.
>          -
>
>          yp: Set to the particular solution found when using variation of
>          parameters.
>
> 3. The "Generated Symbol" Variables
>
> Maxima automatically creates and increments these counters to ensure
> uniqueness in solutions.
>
>    -
>
>    *%c, %k1, %k2*:
>    -
>
>       *Context:* Integration constants generated by ode2 and contrib_ode.
>       -
>
>       *Magic:* %c is for 1st order, %k for 2nd order. They are
>       system-managed constants but appear in your output.
>
>       -
>
>    *%r variables* (e.g., %r1, %r2):
>    -
>
>       *Context:* Set by solve or algsys.
>       -
>
>       *Magic:* These represent arbitrary parameters in the solution of an
>       under-determined system (like a line of solutions). They are
>       tracked in the list %rnum_list.
>
>
> 4. The "History" Variables
>
>    -
>
>    *%*: The result of the *last* command (output).
>
>    -
>
>    *_*: The *input* of the last command.
>    -
>
>    *%%*: The result of the *previous statement* inside a block (e.g., block(a:2,
>    a+2, %% * 10) returns 40).
>    -
>
>    *%th(k)*: The *k-th* previous output (e.g., %th(2) is the one before %
>    ).
>    -
>
>    *%i / %o / %t labels*:
>    -
>
>       %i5: Input #5.
>       -
>
>       %o5: Output #5.
>       -
>
>       %t5: *Intermediate* expressions. These often appear when solving
>       large systems or generating code; Maxima labels a sub-expression %t5
>       and prints it separately to keep the main output readable.
>
> 5. Loop Variables (Not Magical)
>
> It is worth noting that unlike some languages (like Perl's $_ or awk's NR),
> Maxima *does not* have an implicit variable for the current element in a
> map or apply. You must always explicitly name your iterator (e.g., map(lambda([u],
> u^2), [1,2,3])).
>