eQuate It CAS UDFs — Miscellaneous (TI-Nspire CAS)
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1. ca(ans, vars) — Column augment to matrix form
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Define ca(ans, vars) = Prgm
  Local n, i, row, mat
  n := dim(vars)
  Disp "Converting to matrix form:"
  mat := newMat(dim(ans), n)
  For i, 1, dim(ans)
    For j, 1, n
      mat[i, j] := ans[i] | vars[j]
    EndFor
  EndFor
  Disp mat
EndPrgm


2. dsolve(eq, x, lo, hi) — Solve equation in restricted domain
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Define dsolve(eq, x, lo, hi) = Prgm
  Local result
  result := solve(eq, x) | lo <= x and x <= hi
  Disp "Solutions in [", lo, ",", hi, "]:"
  Disp result
EndPrgm


3. graphinfo — Complete graph information
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(Maximal domain)
Define graphinfo(f, x, lo, hi) = Prgm
  Local fp, fpp, xi, yi, stp, poi, ep
  fp := d(f, x)
  fpp := d(fp, x)
  xi := solve(f = 0, x)
  yi := f | x = 0
  stp := solve(fp = 0, x)
  poi := solve(fpp = 0, x)
  Disp "x-intercepts: ", xi
  Disp "y-intercept: ", yi
  Disp "Stationary points at x = ", stp
  For i, 1, dim(stp)
    Disp "  (", stp[i], ", ", f | x = stp[i], ")"
  EndFor
  Disp "POI at x = ", poi
  For i, 1, dim(poi)
    Disp "  (", poi[i], ", ", f | x = poi[i], ")"
  EndFor
  If lo ≠ " " Then
    Disp "Endpoints:"
    Disp "  (", lo, ", ", f | x = lo, ")"
    Disp "  (", hi, ", ", f | x = hi, ")"
  EndIf
EndPrgm


4. trigsolve(eq, x, lo, hi) — Exact trig equation solver
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Define trigsolve(eq, x, lo, hi) = Prgm
  Local result, approx_result, exact, i
  result := solve(eq, x) | lo <= x and x <= hi
  Disp "Solutions in [", lo, ",", hi, "]:"
  Disp result
EndPrgm


5. triginfo(f, x, lo, hi) — Trigonometric function information
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Define triginfo(f, x, lo, hi) = Prgm
  Local fp, maxv, minv, amp, period, mid, xi, yi, stp, asym
  fp := d(f, x)
  Disp "Analysing trig function on [", lo, ",", hi, "]"
  maxv := fMax(f, x) | lo <= x <= hi
  minv := fMin(f, x) | lo <= x <= hi
  amp := (maxv - minv) / 2
  mid := (maxv + minv) / 2
  xi := solve(f = 0, x) | lo <= x <= hi
  yi := f | x = 0
  stp := solve(fp = 0, x) | lo <= x <= hi
  Disp "Amplitude: ", amp
  Disp "Middle value: ", mid
  Disp "Max: ", maxv, "  Min: ", minv
  Disp "x-intercepts: ", xi
  Disp "y-intercept: ", yi
  Disp "Turning points at x = ", stp
  Disp "Endpoints:"
  Disp "  (", lo, ", ", f | x = lo, ")"
  Disp "  (", hi, ", ", f | x = hi, ")"
EndPrgm