544
544
Factors(15) [1,3,5,15]
545
545
Factors(-15) [-1,1,3,5,15]
546
546
Factors(0)+1 ((null)+1)
547
Factors(NextPrime(777777)*NextPrime(888888)) [1,777781,888917,691382753177]
548
Factors(NextPrime(7777777)*NextPrime(8888888)) [1,7777801,8888927,69136305309527]
549
Factors(NextPrime(77777)^2*NextPrime(88888)) [1,77783,88897,6050195089,6914675351,537844192826833]
550
Factors(2^10) [1,2,4,8,16,32,64,128,256,512,1024]
551
Factors(2^5*NextPrime(10000000)) [1,2,4,8,16,32,10000019,20000038,40000076,80000152,160000304,320000608]
547
552
PrimeFactors(15) [3,5]
548
553
MaximalPrimePowerFactors(15) [3,5]
549
554
MaximalPrimePowerFactors(75) [3,25]
1077
1082
IntegerQuotient(-1,3) -1
1078
1083
IntegerQuotient(1,-3) -1
1079
1084
IntegerQuotient([1,2,3],[2,2,2]) [0,1,1]
1085
j=0;(for n=1 to 20 do (for d=1 to 20 do (if n!=(sum r in ColumnsOf(MacaulayRep(n,d)) do nCr(r@(1),r@(2))) then increment j)));j 0
1086
MacaulayRep(27,3) [6,4,1;3,2,1]
1087
MacaulayBound(27,3) 46
1088
MacaulayLowerOperator(27,3) 13
1091
(-2)^(1/3) -1.25992104989
1094
(-2)^(-1/3) -0.793700525984
1097
(-2)^(-2/3) 0.629960524947
1098
KroneckerDelta([1,1,1]) 1
1099
KroneckerDelta([1;1;1]) 1
1100
KroneckerDelta([1;1,1]) 0
1101
KroneckerDelta([10,12]) 0
1102
DiscreteDelta([0,0]) 1
1103
DiscreteDelta([0;0]) 1
1104
DiscreteDelta([0,0;0,1]) 0
1105
DiscreteDelta([1,0;0,0]) 0
1106
LinearRecursiveSequence ([0,1],[1,1],6) 8
1107
LinearRecursiveSequence ([0,1],[1,1],[0,1,2,3,4,5,6]) [0,1,1,2,3,5,8]
1108
LinearRecursiveSequence ([0,1],[1,1],[0,1,2,3,4,5,6]) [0,1,1,2,3,5,8]
1109
LinearRecursiveSequence ([5,7],[1,2],2) 19
1110
LinearRecursiveSequence ([1,3,5],[1,2,-1],3) 2
1111
LinearRecursiveSequence ([1,3,5],[1,2,-1],null)+1 ((null)+1)
1112
prod n=1 to 20 do (A=randint(10,7,7)-4*ones(7,7);IsPositiveSemidefinite(A'*A)) true
1113
prod n=1 to 20 do (A=randint(10,3,7)-4*ones(3,7);IsPositiveSemidefinite(A'*A)) true
1114
prod n=1 to 20 do (A=randint(10,7,7)-4*ones(7,7);(rank(A'*A) < 7) or IsPositiveDefinite(A'*A)) true
1116
sinc(5)==sin(5)/5 true
1117
A=[1;2];B=[3;4;5;6;7];[A,B,0,null,4]+"" "[1,3,0,4;2,4,0,4;1,5,0,4;2,6,0,4;1,7,0,4]"
1118
A=[1,2;3,4];B=[5;6;7];[A,B]+"" "[1,2,5;3,4,6;1,2,7]"
1119
[[1;[1,2]],[3,[7;4]]]+"" "[1,1,3,7;1,2,3,4]"
1120
sum n=0 to 1 by 0.100000001 do n 5.500000045
1121
sum n=0 to 0.95 by 0.1 do n 4.5
1122
sum n=0 to 0.9 by 0.1 do n 4.5
1123
sum n=0 to 1 by 0.1 do n 5.5
1124
for n=0 to 1 by 0.1 do n 1.0
1125
for n=0 to 1 by 0.100000001 do n 1.0
1126
for n=0 to 1 by 0.10000001 do n 0.90000009
1127
for n=1 to 9.99999999999 do n 9.99999999999
1128
FindRootBisection (`(x)=x^2-1,0.5,1.6,10^-20,10000000) [true,1.0,67]
1129
FindRootBisection (`(x)=x^2-1,-1,0.9,10^-20,10000000) [true,-1.0,68]
1130
FindRootBisection (`(x)=x^2-1,0,10^2000,10^-20,1000)@(1) false
1131
FindRootBisection (`(x)=x^2+1,-1,1,0.01,100) FindRootBisection((`(x)=((x^2)+1)),-1,1,0.01,100)
1080
1132
load "nullspacetest.gel" true
1081
1133
load "longtest.gel" true
1082
1134
load "testprec.gel" true