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Expression of type Equals

from the theory of proveit.numbers.absolute_value

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import r, theta
from proveit.logic import Equals
from proveit.numbers import Exp, Mult, Neg, e, i
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Exp(e, Neg(Mult(theta, i)))
expr = Equals(Mult(Neg(r), sub_expr1), Neg(Mult(r, sub_expr1)))
expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")
Passed sanity check: expr matches stored_expr
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\left(\left(-r\right) \cdot \mathsf{e}^{-\left(\theta \cdot \mathsf{i}\right)}\right) = \left(-\left(r \cdot \mathsf{e}^{-\left(\theta \cdot \mathsf{i}\right)}\right)\right)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()()('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 20
operands: 5
4Operationoperator: 17
operand: 8
5ExprTuple7, 12
6ExprTuple8
7Operationoperator: 17
operand: 11
8Operationoperator: 20
operands: 10
9ExprTuple11
10ExprTuple11, 12
11Variable
12Operationoperator: 13
operands: 14
13Literal
14ExprTuple15, 16
15Literal
16Operationoperator: 17
operand: 19
17Literal
18ExprTuple19
19Operationoperator: 20
operands: 21
20Literal
21ExprTuple22, 23
22Variable
23Literal