Example 1 Without Symmetry 

 

> read
 

> `assign`(d, 3); 1
 

`assign`(d, 3) (6.3.1)
 

> `assign`(t, -`/`(7, 8)); -1; `assign`(aMask, `+`(`*`(`/`(1, 2), `*`(`^`(`*`(`+`(`/`(1, `*`(z)), 1, z), `/`(1, 3)), 3), `*`(`+`(1, `-`(`*`(2, `*`(t))), `*`(t, `*`(`+`(`/`(1, `*`(z)), z)))), `*`(`+`(1, ...
`assign`(t, -`/`(7, 8)); -1; `assign`(aMask, `+`(`*`(`/`(1, 2), `*`(`^`(`*`(`+`(`/`(1, `*`(z)), 1, z), `/`(1, 3)), 3), `*`(`+`(1, `-`(`*`(2, `*`(t))), `*`(t, `*`(`+`(`/`(1, `*`(z)), z)))), `*`(`+`(1, ...
`assign`(t, -`/`(7, 8)); -1; `assign`(aMask, `+`(`*`(`/`(1, 2), `*`(`^`(`*`(`+`(`/`(1, `*`(z)), 1, z), `/`(1, 3)), 3), `*`(`+`(1, `-`(`*`(2, `*`(t))), `*`(t, `*`(`+`(`/`(1, `*`(z)), z)))), `*`(`+`(1, ...
`assign`(t, -`/`(7, 8)); -1; `assign`(aMask, `+`(`*`(`/`(1, 2), `*`(`^`(`*`(`+`(`/`(1, `*`(z)), 1, z), `/`(1, 3)), 3), `*`(`+`(1, `-`(`*`(2, `*`(t))), `*`(t, `*`(`+`(`/`(1, `*`(z)), z)))), `*`(`+`(1, ...
 

 

`assign`(aMask, `+`(`*`(`/`(1, 2), `*`(`^`(`+`(`/`(`*`(`/`(1, 3)), `*`(z)), `/`(1, 3), `*`(`/`(1, 3), `*`(z))), 3), `*`(`+`(`/`(11, 4), `-`(`*`(`/`(7, 8), `*`(z))), `-`(`/`(`*`(`/`(7, 8)), `*`(z)))), ...
`assign`(bMask, `*`(`^`(`+`(`/`(`*`(`/`(1, 3)), `*`(z)), `/`(1, 3), `*`(`/`(1, 3), `*`(z))), 2), `*`(`+`(`*`(`/`(313, 384), `*`(z)), `/`(313, 384), `/`(`*`(`/`(211, 960)), `*`(z)), `*`(`/`(211, 960), ...
`assign`(bMask, `*`(`^`(`+`(`/`(`*`(`/`(1, 3)), `*`(z)), `/`(1, 3), `*`(`/`(1, 3), `*`(z))), 2), `*`(`+`(`*`(`/`(313, 384), `*`(z)), `/`(313, 384), `/`(`*`(`/`(211, 960)), `*`(z)), `*`(`/`(211, 960), ...
(6.3.2)
 

> D1IsDual(aMask, bMask, d, sqrt(d)); 1
 

Vector[column](%id = 151319820) (6.3.3)
 

> D1Nu2Mask(aMask, d, 3); 1; D1Nu2Mask(bMask, d, 2); 1
 

 

2.152005751
.9649084550 (6.3.4)
 

> SYM(aMask), SYM(bMask); 1
 

z, z (6.3.5)
 

> `assign`(dualChain, D1GetDualChain(aMask, bMask, d)); 1
`assign`(dualChain, D1GetDualChain(aMask, bMask, d)); 1
 

`assign`(dualChain, [`*`(`^`(`+`(`/`(`*`(`/`(1, 3)), `*`(z)), `/`(1, 3), `*`(`/`(1, 3), `*`(z))), 2), `*`(`+`(`*`(`/`(313, 384), `*`(z)), `/`(313, 384), `/`(`*`(`/`(211, 960)), `*`(z)), `*`(`/`(211, 9...
`assign`(dualChain, [`*`(`^`(`+`(`/`(`*`(`/`(1, 3)), `*`(z)), `/`(1, 3), `*`(`/`(1, 3), `*`(z))), 2), `*`(`+`(`*`(`/`(313, 384), `*`(z)), `/`(313, 384), `/`(`*`(`/`(211, 960)), `*`(z)), `*`(`/`(211, 9...
`assign`(dualChain, [`*`(`^`(`+`(`/`(`*`(`/`(1, 3)), `*`(z)), `/`(1, 3), `*`(`/`(1, 3), `*`(z))), 2), `*`(`+`(`*`(`/`(313, 384), `*`(z)), `/`(313, 384), `/`(`*`(`/`(211, 960)), `*`(z)), `*`(`/`(211, 9...
`assign`(dualChain, [`*`(`^`(`+`(`/`(`*`(`/`(1, 3)), `*`(z)), `/`(1, 3), `*`(`/`(1, 3), `*`(z))), 2), `*`(`+`(`*`(`/`(313, 384), `*`(z)), `/`(313, 384), `/`(`*`(`/`(211, 960)), `*`(z)), `*`(`/`(211, 9...
`assign`(dualChain, [`*`(`^`(`+`(`/`(`*`(`/`(1, 3)), `*`(z)), `/`(1, 3), `*`(`/`(1, 3), `*`(z))), 2), `*`(`+`(`*`(`/`(313, 384), `*`(z)), `/`(313, 384), `/`(`*`(`/`(211, 960)), `*`(z)), `*`(`/`(211, 9...
`assign`(dualChain, [`*`(`^`(`+`(`/`(`*`(`/`(1, 3)), `*`(z)), `/`(1, 3), `*`(`/`(1, 3), `*`(z))), 2), `*`(`+`(`*`(`/`(313, 384), `*`(z)), `/`(313, 384), `/`(`*`(`/`(211, 960)), `*`(z)), `*`(`/`(211, 9...
(6.3.6)
 

> `assign`(tP, P, D1GetDualChainUp(dualChain, d)); -1
`assign`(tP, P, D1GetDualChainUp(dualChain, d)); -1
`assign`(tP, P, D1GetDualChainUp(dualChain, d)); -1
 

test1 (6.3.7)
 

> `assign`(bfilters, D1Polyphase2Mask(tP[1], d)); -1
`assign`(bfilters, D1Polyphase2Mask(tP[1], d)); -1
`assign`(bfilters, D1Polyphase2Mask(tP[1], d)); -1
 

> `assign`(afilters, D1Polyphase2Mask(P[2], d)); -1
 

> simplify(`+`(afilters[1, 1], `-`(aMask))); 1
 

0 (6.3.8)
 

> simplify(`+`(bfilters[1, 1], `-`(bMask))); 1
 

0 (6.3.9)
 

> D1Support(afilters[2, 1]), D1Support(afilters[3, 1]); 1
 

Vector[column](%id = 210501632), Vector[column](%id = 152823536) (6.3.10)
 

> D1Support(bfilters[2, 1]), D1Support(bfilters[3, 1]); 1
 

Vector[column](%id = 152794464), Vector[column](%id = 153423728) (6.3.11)