We take two tcl access scripts, presuming presence of Maxima and PostgreSQL on a system or in the latter case on some system in the network:
proc domaxima { {m} } {
set t "display2d:false;\n$m;"
# return [string range [exec maxima << $t | tail -2 ] 6 end-7]
return [string range [exec maxima -q << $t ] 32 end-7]
#return [exec maxima --real-quiet << $t ]
}
proc dosql {s} {
global db
if {[catch {pg_exec $db $s} reply]} {
puts "sql error : $reply,[pg_result $reply -error]"
return "Error"
}
if {[pg_result $reply -status] == "PGRES_COMMAND_OK"} {
return {}
}
if {[pg_result $reply -status] != "PGRES_TUPLES_OK"} {
puts "sql error: [pg_result $reply -error]"
return "Error"
}
return [pg_result $reply -llist]
# pg_result $reply -clear
return
}
# You could use another with similar results, it appears:
package require pgintcl
# connect to your sql server:
set db [pg_connect -conninfo [list host = 192.168.0.1 user = zxy dbname = somedb password = 0x987654]]
# Now create a table for formulas
dosql "create table formula (f varchar(256))"Now we can try to make a nice database with formulas:
dosql "insert into formula values ([pg_quote "x^2"])" dosql "insert into formula values ([pg_quote "x^3"])"
But we can also use maxima to help us, for instance the optimizer will reorder terms and at request also simplify so we can keep formulas unique for instance:
dosql "insert into formula values ([pg_quote [domaxima "x^4"]])" dosql "insert into formula values ([pg_quote [domaxima "x^3"]])"
Now lets look at the nice lil' list of math work:
foreach i [dosql "select distinct f from formula"] {puts |$i}
|x^2
|x^3
|x^4A more interesting example, a list of repeated derivatives of a products of two functions, a well known formula for case 1:
dosql "create table derivatives (ref varchar(64), f varchar(10000), df varchar(10000))" set i 1; set fo "q(x)*r(x)"; dosql "insert into derivatives values ( [pg_quote "prod$i"], [pg_quote [domaxima $fo]], [pg_quote [domaxima "diff($fo)"]] )" incr i; set fo "diff(q(x)*r(x))"; dosql "insert into derivatives values ( [pg_quote "prod$i"], [pg_quote [domaxima $fo]], [pg_quote [domaxima "diff($fo)"]] )" incr i; set fo "diff(q(x)*r(x))"; dosql "insert into derivatives values ( [pg_quote "prod$i"], [pg_quote [domaxima $fo]], [pg_quote [domaxima "diff($fo)"]] )" incr i; set fo "diff(q(x)*r(x))"; dosql "insert into derivatives values ( [pg_quote "prod$i"], [pg_quote [domaxima $fo]], [pg_quote [domaxima "diff($fo)"]] )"
Of course that could be easily put in a loop, but it's to prove the principle. Now:
% foreach i [dosql "select * from derivatives"] {puts $i}
prod1 q(x)*r(x) (q(x)*'diff(r(x),x,1)+r(x)*'diff(q(x),x,1))*del(x)
prod2 (q(x)*'diff(r(x),x,1)+r(x)*'diff(q(x),x,1))*del(x) {((q(x)*'diff(r(x),x,2)+2*'diff(q(x),x,1)*'diff(r(x),x,1)
+r(x)*'diff(q(x),x,2))
*del(x)
+(q(x)*'diff(r(x),x,1)+r(x)*'diff(q(x),x,1))*'diff(del(x),x,1))
*del(x)}
prod3 (q(x)*'diff(r(x),x,1)+r(x)*'diff(q(x),x,1))*del(x) {((q(x)*'diff(r(x),x,2)+2*'diff(q(x),x,1)*'diff(r(x),x,1)
+r(x)*'diff(q(x),x,2))
*del(x)
+(q(x)*'diff(r(x),x,1)+r(x)*'diff(q(x),x,1))*'diff(del(x),x,1))
*del(x)}
prod4 (q(x)*'diff(r(x),x,1)+r(x)*'diff(q(x),x,1))*del(x) {((q(x)*'diff(r(x),x,2)+2*'diff(q(x),x,1)*'diff(r(x),x,1)
+r(x)*'diff(q(x),x,2))
*del(x)
+(q(x)*'diff(r(x),x,1)+r(x)*'diff(q(x),x,1))*'diff(del(x),x,1))
*del(x)}More intelligently we can now look up in our little database what the general form is of a certain derivative of a product of functions, and what the original was from that derivative (the integral except for a constant), for instance:
(Tcl) 69 % dosql "select ref, f from derivatives where df = [pg_quote "(q(x)*'diff(r(x),x,1)+r(x)*'diff(q(x),x,1))*del(x)"]"
{prod1 q(x)*r(x)}| enter categories here |
|---|