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Functions and commands 415
select Given a Boolean expression in a single variable and a list or
vector, tests each element in the list or vector and returns a list
or vector containing the elements that satisfy the Boolean.
select(Expr, List) or select(Expr, Vector)
Example:
select(x→x>=5,[1,2,6,7]) gives [6,7]
seq Given an expression, a variable defined over an interval, and
a step value, returns a vector containing the sequence
obtained when the expression is evaluated within the given
interval using the given step. If no step is provided, the step
used is 1.
seq(Expr, Var=Interval, [Step])
Example:
seq(2
k
,k=0..8) gives [1,2,4,8,16,32,64,128,256]
seqsolve Similar to rsolve. Given an expression defining a recurrence
relation in terms of n and/or the previous term (x), followed
by a vector of variables and an initial condition for x (the 0th
term), returns the closed form solution (if possible) for the
recurrent sequence. Given three lists, each containing multiple
items of the above nature, solves the system of recurrent
sequences.
seqsolve(Expr, Vector, Condition) or
rsolve(List1, List2, List3)
Example:
seqsolve(2x+n,[x,n],1) gives -n-1+2*2
n
shift_phase Returns the result of applying a phase shift of pi/2 to a
trigonometric expression.
shift_phase(Expr)
Example:
shift_phase(sin(x)) gives -cos((pi+2*x)/2)
signature Returns the signature of a permutation.
signature(Vector)
Example:
signature([2 1 4 5]) returns –1