format

%coerce_bag (op, expr) — Function

Attempts to coerce expr into an expression with op (one of =, #, <, <=, >, >=, [ or matrix) as the top-level operator. It coerces the expression by swapping operands between layers but only if adjacent layers are also lists, matrices or relations. This model assumes that a list of equations, for example, can be viewed as an equation whose sides are lists. Certain combinations, particularly those involving inequalities may not be meaningful, however, so some caution is advised.

%format_piece (piece, nth) — Function

lratsubst’s eqns into expression and the result is formatted at the next layer. Format a given piece of an expression, automatically accounting for subtemplates and the remaining template chain. A specific subtemplate, rather than the next one, can be selected by specifying nth.

format (expr, template1, …) — Function

Each template indicates the desired form for an expression; either the expected form or that into which it will be transformed. At the same time, the indicated form implies a set of pieces; the next template in the chain applies to those pieces. For example, %poly(x) specifies the transformation into a polynomial in x, with the pieces being the coefficients. The passive %frac treats the expression as a fraction; the pieces are the numerator and denominator. Whereas the next template formats all pieces of the previous layer, positional subtemplates may be used to specify formats for each piece individually. This is most useful when the pieces have unique roles and need to be treated differently, such as a fraction’s numerator and denominator.

function_arguments (expr, functions…) — Function

Returns a list of all argument lists for calls to functions in expr.

function_calls (expr, functions…) — Function

Returns a list of all calls in expr involving any of functions.

get_coef (clist, k1, …) — Function

Gets the coefficient from the coefficient list clist corresponding to the keys ki. The keys are matched to variable powers when clist is a %poly, %series or %Taylor form. If clist is a %trig then k1 should be sin or cos and the remaining keys are matched to multipliers.

matching_parts (expr, predicate, args…) — Function

Returns a list of all subexpressions of expr for which the application predicate(piece,args ... ) returns true.

partition_poly (expr, test, v1, …) — Function

Partitions expr into two polynomials; the first is made of those monomials for which the function test returns true and the second is the remainder. The test function is called on the powers of the vi.

partition_series (expr, test, v, O) — Function

partition_Taylor (expr, test, v, O) — Function

Analog to partition_poly for series.

partition_trig (expr, sintest, costest, v1, …) — Function

Trigonometric analog to partition poly; The functions sintest and costest select sine and cosine terms, respectively; each are called on the multipliers of the vi.

uncoef (clist) — Function

Reconstructs the expression from a coefficient list clist. The coefficient list can be any of the coefficient list forms.