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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 e, l
from proveit.logic import InSet
from proveit.numbers import Add, Exp, Interval, Real, 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
expr = InSet(Sum(index_or_indices = [l], summand = frac(one, Exp(l, two)), domain = Interval(Add(e, one), subtract(_two_pow__t_minus_one, one))), 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(\sum_{l = e + 1}^{2^{t - 1} - 1} \frac{1}{l^{2}}\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: 13
operands: 1
1ExprTuple2, 3
2Operationoperator: 4
operand: 6
3Literal
4Literal
5ExprTuple6
6Lambdaparameter: 20
body: 8
7ExprTuple20
8Conditionalvalue: 9
condition: 10
9Operationoperator: 11
operands: 12
10Operationoperator: 13
operands: 14
11Literal
12ExprTuple37, 15
13Literal
14ExprTuple20, 16
15Operationoperator: 27
operands: 17
16Operationoperator: 18
operands: 19
17ExprTuple20, 29
18Literal
19ExprTuple21, 22
20Variable
21Operationoperator: 31
operands: 23
22Operationoperator: 31
operands: 24
23ExprTuple25, 37
24ExprTuple26, 34
25Variable
26Operationoperator: 27
operands: 28
27Literal
28ExprTuple29, 30
29Literal
30Operationoperator: 31
operands: 32
31Literal
32ExprTuple33, 34
33Literal
34Operationoperator: 35
operand: 37
35Literal
36ExprTuple37
37Literal