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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 Add, Exp, Mult, e, i, pi, two
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Mult(two, pi, i, a)
sub_expr2 = Mult(two, pi, i, b)
sub_expr3 = Mult(Add(Mult(two, pi, i, delta), Mult(two, pi, i, theta)), k)
expr = Equals(Mult(Exp(e, sub_expr1), Exp(e, sub_expr3), Exp(e, sub_expr2)), Exp(e, Add(sub_expr1, sub_expr3, sub_expr2)))
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 a} \cdot \mathsf{e}^{\left(\left(2 \cdot \pi \cdot \mathsf{i} \cdot \delta\right) + \left(2 \cdot \pi \cdot \mathsf{i} \cdot \theta\right)\right) \cdot k} \cdot \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot b}\right) = \mathsf{e}^{\left(2 \cdot \pi \cdot \mathsf{i} \cdot a\right) + \left(\left(\left(2 \cdot \pi \cdot \mathsf{i} \cdot \delta\right) + \left(2 \cdot \pi \cdot \mathsf{i} \cdot \theta\right)\right) \cdot k\right) + \left(2 \cdot \pi \cdot \mathsf{i} \cdot b\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: 32
operands: 5
4Operationoperator: 13
operands: 6
5ExprTuple7, 8, 9
6ExprTuple16, 10
7Operationoperator: 13
operands: 11
8Operationoperator: 13
operands: 12
9Operationoperator: 13
operands: 14
10Operationoperator: 27
operands: 15
11ExprTuple16, 17
12ExprTuple16, 18
13Literal
14ExprTuple16, 19
15ExprTuple17, 18, 19
16Literal
17Operationoperator: 32
operands: 20
18Operationoperator: 32
operands: 21
19Operationoperator: 32
operands: 22
20ExprTuple35, 36, 37, 23
21ExprTuple24, 25
22ExprTuple35, 36, 37, 26
23Variable
24Operationoperator: 27
operands: 28
25Variable
26Variable
27Literal
28ExprTuple29, 30
29Operationoperator: 32
operands: 31
30Operationoperator: 32
operands: 33
31ExprTuple35, 36, 37, 34
32Literal
33ExprTuple35, 36, 37, 38
34Variable
35Literal
36Literal
37Literal
38Variable