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Expression of type InSet

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 l
from proveit.logic import InSet
from proveit.numbers import Add, Exp, Real, Sum, frac, one, subtract, two
from proveit.physics.quantum.QPE import _neg_domain, _pos_domain
In [2]:
# build up the expression from sub-expressions
sub_expr1 = [l]
expr = InSet(Add(Sum(index_or_indices = sub_expr1, summand = frac(one, Exp(l, two)), domain = _neg_domain), Sum(index_or_indices = sub_expr1, summand = frac(one, Exp(subtract(l, one), two)), domain = _pos_domain)), Real)
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(\left(\sum_{l = -2^{t - 1} + 1}^{-\left(e + 1\right)} \frac{1}{l^{2}}\right) + \left(\sum_{l = e + 1}^{2^{t - 1}} \frac{1}{\left(l - 1\right)^{2}}\right)\right) \in \mathbb{R}
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: 23
operands: 1
1ExprTuple2, 3
2Operationoperator: 51
operands: 4
3Literal
4ExprTuple5, 6
5Operationoperator: 8
operand: 10
6Operationoperator: 8
operand: 11
7ExprTuple10
8Literal
9ExprTuple11
10Lambdaparameter: 42
body: 12
11Lambdaparameter: 42
body: 14
12Conditionalvalue: 15
condition: 16
13ExprTuple42
14Conditionalvalue: 17
condition: 18
15Operationoperator: 21
operands: 19
16Operationoperator: 23
operands: 20
17Operationoperator: 21
operands: 22
18Operationoperator: 23
operands: 24
19ExprTuple57, 25
20ExprTuple42, 26
21Literal
22ExprTuple57, 27
23Literal
24ExprTuple42, 28
25Operationoperator: 47
operands: 29
26Operationoperator: 32
operands: 30
27Operationoperator: 47
operands: 31
28Operationoperator: 32
operands: 33
29ExprTuple42, 49
30ExprTuple34, 35
31ExprTuple36, 49
32Literal
33ExprTuple41, 45
34Operationoperator: 51
operands: 37
35Operationoperator: 55
operand: 41
36Operationoperator: 51
operands: 39
37ExprTuple40, 57
38ExprTuple41
39ExprTuple42, 54
40Operationoperator: 55
operand: 45
41Operationoperator: 51
operands: 44
42Variable
43ExprTuple45
44ExprTuple46, 57
45Operationoperator: 47
operands: 48
46Variable
47Literal
48ExprTuple49, 50
49Literal
50Operationoperator: 51
operands: 52
51Literal
52ExprTuple53, 54
53Literal
54Operationoperator: 55
operand: 57
55Literal
56ExprTuple57
57Literal