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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 a, b, k, theta
from proveit.logic import Equals
from proveit.numbers import Add, Exp, Mult, e, i, pi, two
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Add(a, b)
sub_expr2 = Exp(e, Mult(two, pi, i, theta))
expr = Equals(Exp(Mult(sub_expr2, sub_expr1), k), Mult(Exp(sub_expr2, k), Exp(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())
\left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \theta} \cdot \left(a + b\right)\right)^{k} = \left((\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \theta})^{k} \cdot \left(a + b\right)^{k}\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: 16
operands: 5
4Operationoperator: 24
operands: 6
5ExprTuple7, 15
6ExprTuple8, 9
7Operationoperator: 24
operands: 10
8Operationoperator: 16
operands: 11
9Operationoperator: 16
operands: 12
10ExprTuple13, 14
11ExprTuple13, 15
12ExprTuple14, 15
13Operationoperator: 16
operands: 17
14Operationoperator: 18
operands: 19
15Variable
16Literal
17ExprTuple20, 21
18Literal
19ExprTuple22, 23
20Literal
21Operationoperator: 24
operands: 25
22Variable
23Variable
24Literal
25ExprTuple26, 27, 28, 29
26Literal
27Literal
28Literal
29Variable