Solving vector equations; is this possible?
Victor Eijkhout <[email protected]> Fri, 1 Jun 2012 07:37:07 +0000
| Newsgroups | gmane.comp.mathematics.axiom.user |
|---|---|
| Message-ID | <[email protected]> |
--===============5666032323828185243== Content-Language: en-US Content-Type: multipart/alternative; boundary="_000_8FD82F71A61442428320FB970733BBCCtaccutexasedu_" --_000_8FD82F71A61442428320FB970733BBCCtaccutexasedu_ Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: quoted-printable Can someone tell me if the following can be solved in Axiom, and hence whet= her I should bother learning the system? I have two equations in vectors of arbitrary dimension: z =3D y + ax (a is = scalar, x,y,z vector) & p^t z =3D 0 (p another vector). Vectors x,y,p are known, vector z and scalar a are unk= nown. Assume no two known vectors are orthogonal. The solution of this is z =3D y + a x where a =3D -(p^t y) / (p^t x). Is this expressible and solvable in Axiom? Victor. --_000_8FD82F71A61442428320FB970733BBCCtaccutexasedu_ Content-Type: text/html; charset="us-ascii" Content-ID: <[email protected]> Content-Transfer-Encoding: quoted-printable <html> <head> <meta http-equiv=3D"Content-Type" content=3D"text/html; charset=3Dus-ascii"= > </head> <body style=3D"word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-lin= e-break: after-white-space; "> Can someone tell me if the following can be solved in Axiom, and hence whet= her I should bother learning the system? <div><span style=3D"color: rgb(80, 0, 80); font-family: Arial, Helvetica, s= ans-serif; font-size: 13px; font-style: normal; font-variant: normal; font-= weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; te= xt-align: -webkit-auto; text-indent: 0px; text-transform: none; white-space= : normal; widows: 2; word-spacing: 0px; -webkit-text-size-adjust: auto; -we= bkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); display:= inline !important; float: none; "><br> </span></div> <div><span style=3D"color: rgb(80, 0, 80); font-family: Arial, Helvetica, s= ans-serif; font-size: 13px; font-style: normal; font-variant: normal; font-= weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; te= xt-align: -webkit-auto; text-indent: 0px; text-transform: none; white-space= : normal; widows: 2; word-spacing: 0px; -webkit-text-size-adjust: auto; -we= bkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); display:= inline !important; float: none; ">I have two equations in vectors of arbitrary dimension: z =3D y + ax (a = is scalar, x,y,z vector) & p^t z =3D 0 </span></div> <div><span style=3D"color: rgb(80, 0, 80); font-family: Arial, Helvetica, s= ans-serif; font-size: 13px; font-style: normal; font-variant: normal; font-= weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; te= xt-align: -webkit-auto; text-indent: 0px; text-transform: none; white-space= : normal; widows: 2; word-spacing: 0px; -webkit-text-size-adjust: auto; -we= bkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); display:= inline !important; float: none; ">(p another vector). Vectors </span><span style=3D"color: rgb(80, 0= , 80); font-family: Arial, Helvetica, sans-serif; font-size: 13px; font-sty= le: normal; font-variant: normal; font-weight: normal; letter-spacing: norm= al; line-height: normal; orphans: 2; text-align: -webkit-auto; text-indent:= 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0= px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; backgro= und-color: rgb(255, 255, 255); display: inline !important; float: none; ">x= ,y,p are known, vector z and scalar a are unknown. A</span><span style=3D"= color: rgb(80, 0, 80); font-family: Arial, Helvetica, sans-serif; font-size= : 13px; font-style: normal; font-variant: normal; font-weight: normal; lett= er-spacing: normal; line-height: normal; orphans: 2; text-align: -webkit-au= to; text-indent: 0px; text-transform: none; white-space: normal; widows: 2;= word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-wid= th: 0px; background-color: rgb(255, 255, 255); display: inline !important; = ">ssume no two known vectors are orthogonal.</span><br style=3D"color: rgb(80, 0, = 80); font-family: Arial, Helvetica, sans-serif; font-size: 13px; font-style= : normal; font-variant: normal; font-weight: normal; letter-spacing: normal= ; line-height: normal; orphans: 2; text-align: -webkit-auto; text-indent: 0= px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px= ; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; backgroun= d-color: rgb(255, 255, 255); "> <br style=3D"color: rgb(80, 0, 80); font-family: Arial, Helvetica, sans-ser= if; font-size: 13px; font-style: normal; font-variant: normal; font-weight:= normal; letter-spacing: normal; line-height: normal; orphans: 2; text-alig= n: -webkit-auto; text-indent: 0px; text-transform: none; white-space: norma= l; widows: 2; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-te= xt-stroke-width: 0px; background-color: rgb(255, 255, 255); "> <span style=3D"color: rgb(80, 0, 80); font-family: Arial, Helvetica, sans-s= erif; font-size: 13px; font-style: normal; font-variant: normal; font-weigh= t: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-al= ign: -webkit-auto; text-indent: 0px; text-transform: none; white-space: nor= mal; widows: 2; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-= text-stroke-width: 0px; background-color: rgb(255, 255, 255); display: inli= ne !important; float: none; ">The solution of this is</span><span style=3D"color: rgb(80, 0, 80); font-famil= y: Arial, Helvetica, sans-serif; font-size: 13px; font-style: normal; font-= variant: normal; font-weight: normal; letter-spacing: normal; line-height: = normal; orphans: 2; text-align: -webkit-auto; text-indent: 0px; text-transf= orm: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-= size-adjust: auto; -webkit-text-stroke-width: 0px; background-color: rgb(25= 5, 255, 255); display: inline !important; float: none; "> z =3D y + a x where a =3D -(p^t y) / (p^t x). </span></div> <div><span style=3D"color: rgb(80, 0, 80); font-family: Arial, Helvetica, s= ans-serif; font-size: 13px; font-style: normal; font-variant: normal; font-= weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; te= xt-align: -webkit-auto; text-indent: 0px; text-transform: none; white-space= : normal; widows: 2; word-spacing: 0px; -webkit-text-size-adjust: auto; -we= bkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); display:= inline !important; float: none; "><br> </span></div> <div><font class=3D"Apple-style-span" color=3D"#500050" face=3D"Arial, Helv= etica, sans-serif"><span class=3D"Apple-style-span" style=3D"font-size: 13p= x;">Is this expressible and solvable in Axiom?</span></font></div> <div><font class=3D"Apple-style-span" color=3D"#500050" face=3D"Arial, Helv= etica, sans-serif"><span class=3D"Apple-style-span" style=3D"font-size: 13p= x;"><br> </span></font></div> <div><font class=3D"Apple-style-span" color=3D"#500050" face=3D"Arial, Helv= etica, sans-serif"><span class=3D"Apple-style-span" style=3D"font-size: 13p= x;">Victor.</span></font></div> <div><font class=3D"Apple-style-span" color=3D"#500050" face=3D"Arial, Helv= etica, sans-serif"><span class=3D"Apple-style-span" style=3D"font-size: 13p= x;"><br> </span></font></div> </body> </html> --_000_8FD82F71A61442428320FB970733BBCCtaccutexasedu_-- --===============5666032323828185243== Content-Type: text/plain; charset="us-ascii" MIME-Version: 1.0 Content-Transfer-Encoding: 7bit Content-Disposition: inline _______________________________________________ Axiom-mail mailing list [email protected] https://lists.nongnu.org/mailman/listinfo/axiom-mail --===============5666032323828185243==--