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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, delta, 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 = Exp(e, Mult(two, pi, i, a))
sub_expr2 = Exp(e, Mult(two, pi, i, k, delta))
sub_expr3 = Exp(e, Mult(two, pi, i, theta, k))
sub_expr4 = Exp(e, Mult(two, pi, i, b))
expr = Equals(Mult(sub_expr1, sub_expr2, sub_expr3, sub_expr4), Mult(sub_expr1, Mult(sub_expr2, sub_expr3), sub_expr4)).with_wrapping_at(2)
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())
\begin{array}{c} \begin{array}{l} \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot a} \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot k \cdot \delta} \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \theta \cdot k} \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot b}\right) =  \\ \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot a} \cdot \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot k \cdot \delta} \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \theta \cdot k}\right) \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot b}\right) \end{array} \end{array}
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.()(2)('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: 28
operands: 5
4Operationoperator: 28
operands: 6
5ExprTuple7, 14, 15, 9
6ExprTuple7, 8, 9
7Operationoperator: 19
operands: 10
8Operationoperator: 28
operands: 11
9Operationoperator: 19
operands: 12
10ExprTuple24, 13
11ExprTuple14, 15
12ExprTuple24, 16
13Operationoperator: 28
operands: 17
14Operationoperator: 19
operands: 18
15Operationoperator: 19
operands: 20
16Operationoperator: 28
operands: 21
17ExprTuple31, 32, 33, 22
18ExprTuple24, 23
19Literal
20ExprTuple24, 25
21ExprTuple31, 32, 33, 26
22Variable
23Operationoperator: 28
operands: 27
24Literal
25Operationoperator: 28
operands: 29
26Variable
27ExprTuple31, 32, 33, 35, 30
28Literal
29ExprTuple31, 32, 33, 34, 35
30Variable
31Literal
32Literal
33Literal
34Variable
35Variable