superset - Maple Help

verify/superset

verify that the first set is a superset of the second

 Calling Sequence verify($\mathrm{expr1}$, $\mathrm{expr2}$, superset) verify($\mathrm{expr1}$, $\mathrm{expr2}$, superset($\mathrm{ver}$))

Parameters

 expr1, expr2 - anything, assumed to be of type set ver - verification for the set operands

Description

 • The verify(expr1, expr2, superset) and verify(expr1, expr2, superset(ver)) calling sequences return true if, for every operand in the second set, expr2, it can be determined that there is an operand in the first set, expr1, that satisfies the relationship ver. If ver is omitted, then equality is used.
 • If true is returned, then it has been determined that each operand of the second set satisfies the relationship with at least one element of the first set. If false is returned, then there is at least one operand in the second set that does not satisfy the relationship (a result of type verify(false)) with each operand in the first set. If neither case can be determined, FAIL is returned.
 • This verification is not symmetric.
 • If either expr1 or expr2 is not of type set, then false is returned.

Examples

 > $\mathrm{verify}\left(\left\{a,b,c,d,e\right\},\left\{a,b,c\right\},'\mathrm{superset}'\right)$
 ${\mathrm{true}}$ (1)
 > $\mathrm{verify}\left(\left\{a,b,c,d,e\right\},\left\{a,b,c,f\right\},'\mathrm{superset}'\right)$
 ${\mathrm{false}}$ (2)
 > $\mathrm{verify}\left(\left\{a,b,{x}^{2}-x\right\},\left\{a,b,x\left(x-1\right)\right\},'\mathrm{superset}'\right)$
 ${\mathrm{false}}$ (3)
 > $\mathrm{verify}\left(\left\{a,b,{x}^{2}-x\right\},\left\{a,b,x\left(x-1\right)\right\},'\mathrm{superset}\left(\mathrm{expand}\right)'\right)$
 ${\mathrm{true}}$ (4)
 > $\mathrm{verify}\left(\left\{a,b,c,{x}^{2}-x\right\},\left\{a,b,x\left(x-1\right)\right\},'\mathrm{superset}\left(\mathrm{expand}\right)'\right)$
 ${\mathrm{true}}$ (5)
 > $\mathrm{verify}\left(\left\{0.102221,0.2334\right\},\left\{0.10222,0.2333\right\},'\mathrm{superset}'\right)$
 ${\mathrm{false}}$ (6)
 > $\mathrm{verify}\left(\left\{0.102221,0.2334\right\},\left\{0.10222,0.2333\right\},'\mathrm{superset}\left(\mathrm{float}\left({10}^{6}\right)\right)'\right)$
 ${\mathrm{true}}$ (7)