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Expression of type Equals

from the theory of proveit.numbers.multiplication

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 k, theta
from proveit.logic import Equals
from proveit.numbers import Exp, Mult, e, i, pi, two
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Mult(two, pi, i, theta)
expr = Equals(Exp(Exp(e, sub_expr1), k), Exp(e, Mult(sub_expr1, k)))
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())
(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \theta})^{k} = \mathsf{e}^{\left(2 \cdot \pi \cdot \mathsf{i} \cdot \theta\right) \cdot k}
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: 9
operands: 5
4Operationoperator: 9
operands: 6
5ExprTuple7, 14
6ExprTuple12, 8
7Operationoperator: 9
operands: 10
8Operationoperator: 15
operands: 11
9Literal
10ExprTuple12, 13
11ExprTuple13, 14
12Literal
13Operationoperator: 15
operands: 16
14Variable
15Literal
16ExprTuple17, 18, 19, 20
17Literal
18Literal
19Literal
20Variable