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Online Algebra Calculator
Many of users do not use powerful Maxima computer algebra system for systematic work, but for ad hoc algebraic calculations – equations, functions, matrixes, etc. only. To do this job, it is not useful to download the whole application from a web site.
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Run Example
(%i1)intervals(items):=block([result], result: if (emptyp(items)) then [] else if(listp(items)) then if(emptyp(rest(items))) then [] else cons(cons(first(items), [second(items)]), intervals(rest(items)))); (%o1) intervals(items) := block([result], result : if emptyp(items) then [] else (if listp(items) then (if emptyp(rest(items)) then [] else cons(cons(first(items), [second(items)]), intervals(rest(items)))))) (%i2) intervals(makelist(n, n, 1, 10)); (%o2) [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10]] (%i3) intervals(makelist(n, n, 1, 11)); (%o3) [[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11]] (%i4) ans:errcatch(find_root(sin(x), x, 2, 3)); find_root: function has same sign at endpoints: f(2.0) = 0.90929742682568, f(3.0) = 0.14112000805987 (%o4) [] (%i5) ans; (%o5) [] (%i6) seq(start,stop,stepping,[shift]) := block([ n, y:[], shift: (if (not(emptyp(shift))) then float(first(shift)) else (0.0)) ], (n:floor((float(stop-start)/float(stepping)))), (if (start < stop) then (y:flatten(append([y], makelist(float(start+shift+(stepping*(i-start))), i, start, n+start)))) else (y:flatten(append([y], makelist(-(float(stop-shift-(stepping*(i-stop)))), i, -(n+stop), stop))))) (if (n> 1.0) then return(y) else return([]))); (%o6) seq(start, stop, stepping, [shift]) := block([n, y : [], shift : if not emptyp(shift) then float(first(shift)) float(stop - start) else 0.0], n : floor(-------------------), float(stepping) if start < stop then y : flatten(append([y], makelist(float(start + shift + stepping (i - start)), i, start, n + start))) else y : flatten(append([y], makelist(- float(stop - shift - stepping (i - stop)), i, - (n + stop), stop)))(if n > 1.0 then return(y) else return([]))) (%i7) intervals(seq(0,7,1)); (%o7) [[0.0, 1.0], [1.0, 2.0], [2.0, 3.0], [3.0, 4.0], [4.0, 5.0], [5.0, 6.0], [6.0, 7.0]] (%i8) ans:[]; (%o8) [] (%i9) %pi; (%o9) %pi (%i10) %pi, numer; (%o10) 3.141592653589793 (%i11) 2*3.14159/%pi; 6.28318 (%o11) ------- %pi (%i12) block([ans:[]], errormsg:false, for i in intervals(seq(0, 7, 1)) do ans:(append(ans, errcatch(find_root(sin(x), x, first(i), second(i))))), errormsg:true, return(ans)); (%o12) [0.0, 3.141592653589793, 6.283185307179586] (%i13)
Run Example
seq(start,stop,stepping,[shift]) := block([ n, y:[], shift: (if (not(emptyp(shift))) then float(first(shift)) else (0.0)) ], (n:floor((float(stop-start)/float(stepping)))), (if (start < stop) then (y:flatten(append([y], makelist(float(start+shift+(stepping*(i-start))), i, start, n+start)))) else (y:flatten(append([y], makelist(-(float(stop-shift-(stepping*(i-stop)))), i, -(n+stop), stop))))) (if (n> 1.0) then return(y) else return([]))); (%o1) seq(start, stop, stepping, [shift]) := block([n, y : [], shift : if not emptyp(shift) then float(first(shift)) float(stop - start) else 0.0], n : floor(-------------------), float(stepping) if start < stop then y : flatten(append([y], makelist(float(start + shift + stepping (i - start)), i, start, n + start))) else y : flatten(append([y], makelist(- float(stop - shift - stepping (i - stop)), i, - (n + stop), stop)))(if n > 1.0 then return(y) else return([]))) (%i2) kill(pairs); (%o2) done (%i3) pairs(items):=block([result],result:if (emptyp(items)) then [] elseif (listp(items)) then if(emptyp(rest(items))) then cons(last(items), []) else cons(cons(first(items), [second(items)]), [pairs(rest(rest(items)))])); (%o3) pairs(items) := block([result], result : if emptyp(items) then [] elseif listp(items) then (if emptyp(rest(items)) then cons(last(items), []) else cons(cons(first(items), [second(items)]), [pairs(rest(rest(items)))]))) (%i4) pairs([1, 2, 3, 4, 5]); (%o4) [[1, 2], [[3, 4], [5]]] (%i5) kill(pairs); (%o5) done (%i6) pairs(items):=block([result],result:if (emptyp(items)) then [] elseif (listp(items)) then if(emptyp(rest(items))) then [last(items), []] else cons(cons(first(items), [second(items)]), [pairs(rest(rest(items)))])); (%o6) pairs(items) := block([result], result : if emptyp(items) then [] elseif listp(items) then (if emptyp(rest(items)) then [last(items), []] else cons(cons(first(items), [second(items)]), [pairs(rest(rest(items)))]))) (%i7) pairs([1, 2, 3, 4, 5]); (%o7) [[1, 2], [[3, 4], [5, []]]] (%i8) first(pairs(seq(1, 10, 1))); (%o8) [1.0, 2.0] (%i9) test([list]):=map(lambda([x], [first(x), second(x)]),list); (%o9) test([list]) := map(lambda([x], [first(x), second(x)]), list) (%i10) find_root(sin(x), x, 0, %pi); (%o10) 0.0 (%i11)
Run Example
kill(lastdigits,pidigits, a, b); (%o1) done (%i2) ratprint:false; (%o2) false (%i3) pidigits(prec):=block([fpprec:prec+1], ratprint:false, bftorat:false, ratepsilon:2.0e-16, float2bf:false, ans:float((%pi-mod(%pi, 10^(-prec)))), return(ans)); (%o3) pidigits(prec) := block([fpprec : prec + 1], ratprint : false, bftorat : false, ratepsilon : 2.0E-16, float2bf : false, - prec ans : float(%pi - mod(%pi, 10 )), return(ans)) (%i4) lastdigits(fnum, lastn):=block([m:rat(fnum), n:lastn, ans], /* it doesn't help when lastn is bigger than the total digits in fnum it returns the whole digits in fnum anyway without erroring! and fnum=%pi stuff works only upto 8 digits cause num(rat(fnum)) has somuch only! */ratprint:false, ratio(num):=block([k, a], ratprint:false, for k:1 thru fpprec do (a:10^k/ratdenom(num), if(integerp(a)) then return(a))), ratepsilon:2.0e-16, bftorat:false, ans:mod(ratio(fnum)*num(m), (10^n))/(ratio(fnum)*denom(m)), return(float(ans))); (%o4) lastdigits(fnum, lastn) := block([m : rat(fnum), n : lastn, ans], ratprint : false, ratio(num) := block([k, a], ratprint : false, k 10 for k thru fpprec do (a : -------------, if integerp(a) then return(a))), ratdenom(num) n mod(ratio(fnum) num(m), 10 ) ratepsilon : 2.0E-16, bftorat : false, ans : ----------------------------, ratio(fnum) denom(m) return(float(ans))) (%i5) lastdigits(4.1459, 5); (%o5) 4.14590001103631 (%i6) lastdigits(3.1459, 3); (%o6) 0.0459 (%i7) b:pidigits(5); (%o7) 3.14159 (%i8) lastdigits(3.14159, 3); (%o8) 0.00159 (%i9) lastdigits(pidigits(5), 3); (%o9) 0.00159 (%i10) pidigits(6); (%o10) 3.141592 (%i11) lastdigits(pidigits(6), 3); (%o11) 5.9199999999999997E-4 (%i12) lastdigits(4.14592, 3); (%o12) 0.00592 (%i13) lastdigits(b, 3); (%o13) 0.00159 (%i14) a:[0, float(%pi)]; (%o14) [0, 3.141592653589793] (%i15) a; (%o15) [0, 3.141592653589793] (%i16) delete(pidigits(16), a); (%o16) [0] (%i17) delete(pidigits(fpprec), a); (%o17) [0] (%i18) delete(pidigits(fpprec), [0, float(%pi)]); (%o18) [0] (%i19) intervals(items, [granul]):=block([ start:first(items), stop:last(items), ans:[], granul:(if not(emptyp(granul)) then first(granul) else 1) ], ratprint:false, if (emptyp(items)) then [] elseif(listp(items)) then if(emptyp(rest(items))) then [] else while(float(rat(start))< float(rat(stop))) do (ans:delete([], delete([float(rat(stop)), float(rat(stop+granul))], if(float(rat(start+granul))> float(rat(stop))) then return() else append(ans, [cons(float(rat(start)), [float(rat(start+granul))])]))), start:float(rat(start+granul))), return(ans)); (%o19) intervals(items, [granul]) := block([start : first(items), stop : last(items), ans : [], granul : if not emptyp(granul) then first(granul) else 1], ratprint : false, if emptyp(items) then [] elseif listp(items) then (if emptyp(rest(items)) then [] else (while float(rat(start)) < float(rat(stop)) do (ans : delete([], delete([float(rat(stop)), float(rat(stop + granul))], if float(rat(start + granul)) > float(rat(stop)) then return() else append(ans, [cons(float(rat(start)), [float(rat(start + granul))])]))), start : float(rat(start + granul))))), return(ans)) (%i20) intervals([0, 2*%pi], %pi); (%o20) [[0.0, 3.141592653589793], [3.141592653589793, 6.283185307179585]] (%i21) delete(pidigits(fpprec), intervals([0, 2*%pi], %pi)); (%o21) [[0.0, 3.141592653589793], [3.141592653589793, 6.283185307179585]] (%i22)
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