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Expression of type Equals

from the theory of proveit.physics.quantum.QPE

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 e, l
from proveit.logic import Equals
from proveit.numbers import Add, Exp, Interval, Mult, Sum, frac, one, subtract, two
from proveit.physics.quantum.QPE import _two_pow__t_minus_one
In [2]:
# build up the expression from sub-expressions
sub_expr1 = Sum(index_or_indices = [l], summand = frac(one, Exp(l, two)), domain = Interval(Add(e, one), subtract(_two_pow__t_minus_one, one)))
expr = Equals(Mult(Add(one, one), sub_expr1), Add(sub_expr1, sub_expr1)).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(\left(1 + 1\right) \cdot \left(\sum_{l = e + 1}^{2^{t - 1} - 1} \frac{1}{l^{2}}\right)\right) =  \\ \left(\left(\sum_{l = e + 1}^{2^{t - 1} - 1} \frac{1}{l^{2}}\right) + \left(\sum_{l = e + 1}^{2^{t - 1} - 1} \frac{1}{l^{2}}\right)\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: 5
operands: 6
4Operationoperator: 38
operands: 7
5Literal
6ExprTuple8, 9
7ExprTuple9, 9
8Operationoperator: 38
operands: 10
9Operationoperator: 11
operand: 13
10ExprTuple44, 44
11Literal
12ExprTuple13
13Lambdaparameter: 27
body: 15
14ExprTuple27
15Conditionalvalue: 16
condition: 17
16Operationoperator: 18
operands: 19
17Operationoperator: 20
operands: 21
18Literal
19ExprTuple44, 22
20Literal
21ExprTuple27, 23
22Operationoperator: 34
operands: 24
23Operationoperator: 25
operands: 26
24ExprTuple27, 36
25Literal
26ExprTuple28, 29
27Variable
28Operationoperator: 38
operands: 30
29Operationoperator: 38
operands: 31
30ExprTuple32, 44
31ExprTuple33, 41
32Variable
33Operationoperator: 34
operands: 35
34Literal
35ExprTuple36, 37
36Literal
37Operationoperator: 38
operands: 39
38Literal
39ExprTuple40, 41
40Literal
41Operationoperator: 42
operand: 44
42Literal
43ExprTuple44
44Literal