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Solves a system of equations

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Issue #67. Solves a system of equations of two variables (R^2)
This commit is contained in:
ElRoberto13
2020-10-16 01:27:03 -04:00
parent c767d09ac8
commit 4505fc8974
1 changed files with 48 additions and 1 deletions
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49
mathgenerator/mathgen.py
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@@ -296,6 +296,51 @@ def simplifyRadicalFunc(range_x = 100):
(f"sqrt({inside})" if inside != 1 else "")
return problem, solution
def systemOfEquationsFunc(range_x = 10, range_y = 10, coeff_mult_range=10):
# Generate solution point first
x = random.randint(-range_x, range_x)
y = random.randint(-range_y, range_y)
# Start from reduced echelon form (coeffs 1)
c1 = [1, 0, x]
c2 = [0, 1, y]
def randNonZero():
return random.choice([i for i in range(-coeff_mult_range, coeff_mult_range)
if i != 0])
# Add random (non-zero) multiple of equations (rows) to each other
c1_mult = randNonZero()
c2_mult = randNonZero()
new_c1 = [c1[i] + c1_mult * c2[i] for i in range(len(c1))]
new_c2 = [c2[i] + c2_mult * c1[i] for i in range(len(c2))]
# For extra randomness, now add random (non-zero) multiples of original rows
# to themselves
c1_mult = randNonZero()
c2_mult = randNonZero()
new_c1 = [new_c1[i] + c1_mult * c1[i] for i in range(len(c1))]
new_c2 = [new_c2[i] + c2_mult * c2[i] for i in range(len(c2))]
def coeffToFuncString(coeffs):
# lots of edge cases for perfect formatting!
x_sign = '-' if coeffs[0] < 0 else ''
# No redundant 1s
x_coeff = str(abs(coeffs[0])) if abs(coeffs[0]) != 1 else ''
# If x coeff is 0, dont include x
x_str = f'{x_sign}{x_coeff}x' if coeffs[0] != 0 else ''
# if x isn't included and y is positive, dont include operator
op = ' - ' if coeffs[1] < 0 else (' + ' if x_str != '' else '')
# No redundant 1s
y_coeff = abs(coeffs[1]) if abs(coeffs[1]) != 1 else ''
# Don't include if 0, unless x is also 0 (probably never happens)
y_str = f'{y_coeff}y' if coeffs[1] != 0 else ('' if x_str != '' else '0')
return f'{x_str}{op}{y_str} = {coeffs[2]}'
problem = f"{coeffToFuncString(new_c1)}, {coeffToFuncString(new_c2)}"
solution = f"x = {x}, y = {y}"
return problem, solution
# Add random (non-zero) multiple of equations to each other
# || Class Instances
#Format is:
@@ -322,4 +367,6 @@ areaOfTriangle = Generator("Area of Triangle", 18, "Area of Triangle with side l
doesTriangleExist = Generator("Triangle exists check", 19, "Does triangle with sides a, b and c exist?","Yes/No", isTriangleValidFunc)
midPointOfTwoPoint=Generator("Midpoint of the two point", 20,"((X1,Y1),(X2,Y2))=","((X1+X2)/2,(Y1+Y2)/2)",MidPointOfTwoPointFunc)
factoring = Generator("Subtraction", 21, "x^2+(x1+x2)+x1*x2", "(x-x1)(x-x2)", factoringFunc)
simplifyRadical = Generator("Simplify a Radical", 22, "sqrt(72)", "6sqrt(2)", simplifyRadicalFunc)
simplifyRadical = Generator("Simplify a Radical", 22, "sqrt(72)", "6sqrt(2)", simplifyRadicalFunc)
systemOfEquations = Generator("Solve a System of Equations in R^2", 23, "2x + 5y = 13, -3x - 3y = -6", "x = -1, y = 3",
systemOfEquationsFunc)