September 22, 1987 11:02:45 am PDT SACExamples.tioga Let's do some examples of SAC-2 computations with CaminoReal. 1. Polynomial Greatest Common Divisors Let's compute the gcd of two polynomials using SAC-2. Put this one into a CaminoReal tool: X Then put this one into a CaminoReal tool: X . Then primary select the first one, copy select the second, hit the "OpPrimary" button, and select "gcd". Watch the file transfers in the Terminal Viewer, and result comes back as: X . Just for fun, let's factor these polynomials (need to use Reduce for this at the moment): X This runs for a long time (> 15 minutes) without returning. Next try X This one took about 27 minutes, but curious thing is that Reduce says its irreducible. And it is easy to see that X-1 doesn't divide it, since evaluation at X=1 yields -59. Hence SAC-2 gcd above clearly wrong; probably a result of the displayed form giving the wrong idea of what Meddle has actually stored internally. Ę*p˜Ileft˜"Icenter˜LšĐblœ˜J–Y57.71739 pt leading 53.9526 pt topLeading 53.9526 pt topIndent 27.76479 pt bottomLeading šĎl=˜=headšœ&˜&J–Y57.71739 pt leading 53.9526 pt topLeading 53.9526 pt topIndent 27.76479 pt bottomLeading šž[˜[J• CharPropsČArtwork MeddleExprPostfixU16.4349 pt leading 28.182 pt topLeading 28.182 pt topIndent 12.2529 pt bottomLeading MeddleExpr8CaminoRealExpressionRepresentationVersion1.1 (CMPD $difference {$subtrahend (CMPD $sum {$addend (CMPD $difference {$subtrahend (CMPD $difference {$subtrahend (CMPD $difference {$subtrahend (CMPD $difference {$subtrahend (CMPD $sum {$addend (CMPD $sum {$addend (CMPD $difference {$subtrahend (CMPD $negation {$a (CMPD $product {$multiplier (ATOM $integer "91")} {$multiplicand (CMPD $pow {$base (ATOM $variable "X")} {$exponent (ATOM $integer "99")})})})} {$minuend (CMPD $product {$multiplier (ATOM $integer "6")} {$multiplicand (CMPD $pow {$base (ATOM $variable "X")} {$exponent (ATOM $integer "89")})})})} {$augend (CMPD $product {$multiplier (ATOM $integer "34")} {$multiplicand (CMPD $pow {$base (ATOM $variable "X")} {$exponent (ATOM $integer "80")})})})} {$augend (CMPD $product {$multiplier (ATOM $integer "20")} {$multiplicand (CMPD $pow {$base (ATOM $variable "X")} {$exponent (ATOM $integer "76")})})})} {$minuend (CMPD $product {$multiplier (ATOM $integer "56")} {$multiplicand (CMPD $pow {$base (ATOM $variable "X")} {$exponent (ATOM $integer "54")})})})} {$minuend (CMPD $product {$multiplier (ATOM $integer "25")} {$multiplicand (CMPD $pow {$base (ATOM $variable "X")} {$exponent (ATOM $integer "52")})})})} {$minuend (CMPD $product {$multiplier (ATOM $integer "86")} {$multiplicand (CMPD $pow {$base (ATOM $variable "X")} {$exponent (ATOM $integer "44")})})})} {$minuend (CMPD $product {$multiplier (ATOM $integer "17")} {$multiplicand (CMPD $pow {$base (ATOM $variable "X")} {$exponent (ATOM $integer "33")})})})} {$augend (CMPD $product {$multiplier (ATOM $integer "70")} {$multiplicand (CMPD $pow {$base (ATOM $variable "X")} {$exponent (ATOM $integer "31")})})})} {$minuend (ATOM $integer "17")}) MeddlePtSize15–ˆ16.4349 pt the leading 2 .copy .gt 3 1 .roll .ifelse leading 28.182 pt the topLeading 2 .copy .gt 3 1 .roll .ifelse topLeading 28.182 pt the topIndent 2 .copy .gt 3 1 .roll .ifelse topIndent 12.2529 pt the bottomLeading 2 .copy .gt 3 1 .roll .ifelse bottomLeading šœ˜J–Y46.69613 pt leading 37.4999 pt topLeading 37.4999 pt topIndent 33.19622 pt bottomLeading šž)˜)J–ÍArtwork MeddleExprPostfixW16.4522 pt leading 28.1993 pt topLeading 28.1993 pt topIndent 12.2529 pt bottomLeading MeddleExpr9CaminoRealExpressionRepresentationVersion1.1 (CMPD $difference {$subtrahend (CMPD $sum {$addend (CMPD $sum {$addend (CMPD $sum {$addend (CMPD $difference {$subtrahend (CMPD $difference {$subtrahend (CMPD $difference {$subtrahend (CMPD $difference {$subtrahend (CMPD $difference {$subtrahend (CMPD $negation {$a (CMPD $product {$multiplier (ATOM $integer "16")} {$multiplicand (CMPD $pow {$base (ATOM $variable "X")} {$exponent (ATOM $integer "95")})})})} {$minuend (CMPD $product {$multiplier (ATOM $integer "46")} {$multiplicand (CMPD $pow {$base (ATOM $variable "X")} {$exponent (ATOM $integer "84")})})})} {$minuend (CMPD $product {$multiplier (ATOM $integer "38")} {$multiplicand (CMPD $pow {$base (ATOM $variable "X")} {$exponent (ATOM $integer "76")})})})} {$minuend (CMPD $product {$multiplier (ATOM $integer "88")} {$multiplicand (CMPD $pow {$base (ATOM $variable "X")} {$exponent (ATOM $integer "74")})})})} {$minuend (CMPD $product {$multiplier (ATOM $integer "81")} {$multiplicand (CMPD $pow {$base (ATOM $variable "X")} {$exponent (ATOM $integer "72")})})})} {$minuend (CMPD $product {$multiplier (ATOM $integer "21")} {$multiplicand (CMPD $pow {$base (ATOM $variable "X")} {$exponent (ATOM $integer "52")})})})} {$augend (CMPD $product {$multiplier (ATOM $integer "91")} {$multiplicand (CMPD $pow {$base (ATOM $variable "X")} {$exponent (ATOM $integer "49")})})})} {$augend (CMPD $product {$multiplier (ATOM $integer "96")} {$multiplicand (CMPD $pow {$base (ATOM $variable "X")} {$exponent (ATOM $integer "25")})})})} {$augend (CMPD $product {$multiplier (ATOM $integer "64")} {$multiplicand (CMPD $pow {$base (ATOM $variable "X")} {$exponent (ATOM $integer "10")})})})} {$minuend (ATOM $integer "20")}) MeddlePtSize15–Š16.4522 pt the leading 2 .copy .gt 3 1 .roll .ifelse leading 28.1993 pt the topLeading 2 .copy .gt 3 1 .roll .ifelse topLeading 28.1993 pt the topIndent 2 .copy .gt 3 1 .roll .ifelse topIndent 12.2529 pt the bottomLeading 2 .copy .gt 3 1 .roll .ifelse bottomLeading ˜J–W16.4522 pt leading 28.1993 pt topLeading 28.1993 pt topIndent 12.2529 pt bottomLeading šž´˜´J–„Artwork MeddleExprPostfixN11.15 pt leading 22.95 pt topLeading 22.95 pt topIndent 12.2 pt bottomLeading MeddleExprzCaminoRealExpressionRepresentationVersion1.1 (CMPD $sum {$addend (ATOM $variable "X")} {$augend (ATOM $integer "1")}) MeddlePtSize15–11.15 pt the leading 2 .copy .gt 3 1 .roll .ifelse leading 22.95 pt the topLeading 2 .copy .gt 3 1 .roll .ifelse topLeading 22.95 pt the topIndent 2 .copy .gt 3 1 .roll .ifelse topIndent 12.2 pt the bottomLeading 2 .copy .gt 3 1 .roll .ifelse bottomLeading ˜J–W16.4522 pt leading 28.1993 pt topLeading 28.1993 pt topIndent 12.2529 pt bottomLeading šžY˜YJ–ŽArtwork MeddleExprPostfix[20.82431 pt leading 29.82549 pt topLeading 29.82549 pt topIndent 14.99882 pt bottomLeading MeddleExprxCaminoRealExpressionRepresentationVersion1.1 (CMPD $unaryFunction {$f (ATOM $variable "factorize")} {$arg1 (CMPD $difference {$subtrahend (CMPD $sum {$addend (CMPD $difference {$subtrahend (CMPD $difference {$subtrahend (CMPD $difference {$subtrahend (CMPD $difference {$subtrahend (CMPD $sum {$addend (CMPD $sum {$addend (CMPD $difference {$subtrahend (CMPD $negation {$a (CMPD $product {$multiplier (ATOM $integer "91")} {$multiplicand (CMPD $pow {$base (ATOM $variable "X")} {$exponent (ATOM $integer "99")})})})} {$minuend (CMPD $product {$multiplier (ATOM $integer "6")} {$multiplicand (CMPD $pow {$base (ATOM $variable "X")} {$exponent (ATOM $integer "89")})})})} {$augend (CMPD $product {$multiplier (ATOM $integer "34")} {$multiplicand (CMPD $pow {$base (ATOM $variable "X")} {$exponent (ATOM $integer "80")})})})} {$augend (CMPD $product {$multiplier (ATOM $integer "20")} {$multiplicand (CMPD $pow {$base (ATOM $variable "X")} {$exponent (ATOM $integer "76")})})})} {$minuend (CMPD $product {$multiplier (ATOM $integer "56")} {$multiplicand (CMPD $pow {$base (ATOM $variable "X")} {$exponent (ATOM $integer "54")})})})} {$minuend (CMPD $product {$multiplier (ATOM $integer "25")} {$multiplicand (CMPD $pow {$base (ATOM $variable "X")} {$exponent (ATOM $integer "52")})})})} {$minuend (CMPD $product {$multiplier (ATOM $integer "86")} {$multiplicand (CMPD $pow {$base (ATOM $variable "X")} {$exponent (ATOM $integer "44")})})})} {$minuend (CMPD $product {$multiplier (ATOM $integer "17")} {$multiplicand (CMPD $pow {$base (ATOM $variable "X")} {$exponent (ATOM $integer "33")})})})} {$augend (CMPD $product {$multiplier (ATOM $integer "70")} {$multiplicand (CMPD $pow {$base (ATOM $variable "X")} {$exponent (ATOM $integer "31")})})})} {$minuend (ATOM $integer "17")})}) MeddlePtSize15–Ž20.82431 pt the leading 2 .copy .gt 3 1 .roll .ifelse leading 29.82549 pt the topLeading 2 .copy .gt 3 1 .roll .ifelse topLeading 29.82549 pt the topIndent 2 .copy .gt 3 1 .roll .ifelse topIndent 14.99882 pt the bottomLeading 2 .copy .gt 3 1 .roll .ifelse bottomLeading ˜J–W16.4522 pt leading 28.1993 pt topLeading 28.1993 pt topIndent 12.2529 pt bottomLeading šžD˜DJ–Ž20.84335 pt the leading 2 .copy .gt 3 1 .roll .ifelse leading 29.84452 pt the topLeading 2 .copy .gt 3 1 .roll .ifelse topLeading 29.84452 pt the topIndent 2 .copy .gt 3 1 .roll .ifelse topIndent 14.99882 pt the bottomLeading 2 .copy .gt 3 1 .roll .ifelse bottomLeading –ĂArtwork MeddleExprPostfix‚20.84335 pt the leading 2 .copy .gt 3 1 .roll .ifelse leading 29.84452 pt the topLeading 2 .copy .gt 3 1 .roll .ifelse topLeading 29.84452 pt the topIndent 2 .copy .gt 3 1 .roll .ifelse topIndent 14.99882 pt the bottomLeading 2 .copy .gt 3 1 .roll .ifelse bottomLeading MeddleExpryCaminoRealExpressionRepresentationVersion1.1 (CMPD $unaryFunction {$f (ATOM $variable "factorize")} {$arg1 (CMPD $difference {$subtrahend (CMPD $sum {$addend (CMPD $sum {$addend (CMPD $sum {$addend (CMPD $difference {$subtrahend (CMPD $difference {$subtrahend (CMPD $difference {$subtrahend (CMPD $difference {$subtrahend (CMPD $difference {$subtrahend (CMPD $negation {$a (CMPD $product {$multiplier (ATOM $integer "16")} {$multiplicand (CMPD $pow {$base (ATOM $variable "X")} {$exponent (ATOM $integer "95")})})})} {$minuend (CMPD $product {$multiplier (ATOM $integer "46")} {$multiplicand (CMPD $pow {$base (ATOM $variable 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{$multiplier (ATOM $integer "64")} {$multiplicand (CMPD $pow {$base (ATOM $variable "X")} {$exponent (ATOM $integer "10")})})})} {$minuend (ATOM $integer "20")})}) MeddlePtSize15˜J–Ž20.84335 pt the leading 2 .copy .gt 3 1 .roll .ifelse leading 29.84452 pt the topLeading 2 .copy .gt 3 1 .roll .ifelse topLeading 29.84452 pt the topIndent 2 .copy .gt 3 1 .roll .ifelse topIndent 14.99882 pt the bottomLeading 2 .copy .gt 3 1 .roll .ifelse bottomLeading šžž˜žJ–W16.4522 pt leading 28.1993 pt topLeading 28.1993 pt topIndent 12.2529 pt bottomLeading ˜J–[20.82431 pt leading 29.82549 pt topLeading 29.82549 pt topIndent 14.99882 pt bottomLeading ˜J–[28.28012 pt leading 33.62128 pt topLeading 33.62128 pt topIndent 18.65884 pt bottomLeading šĎf˜J–Y53.56988 pt leading 41.7858 pt topLeading 41.7858 pt topIndent 35.78408 pt bottomLeading ˜J–Z59.3254 pt leading 55.56061 pt topLeading 55.56061 pt topIndent 27.76479 pt bottomLeading ˜—J˜—…—Ě.B